Reflection laws & ray diagrams | Light | Physics class 10 | Khan Academy

Summary

This educational video script delves into the laws of reflection, focusing on the second law that equates the angle of incidence to the angle of reflection. It applies these principles to determine the nature and position of images formed by concave and convex mirrors. The discussion includes how specific rays behave when interacting with mirrors, such as those parallel to the principal axis, through the focus, and at the center of curvature. The script concludes with examples of how images appear in different scenarios, including virtual and real images, and their positions relative to the mirror's focal points.

Takeaways

• 🔍 The first law of reflection is that the incident ray, the normal, and the reflected ray all lie in the same plane, but it's not particularly useful for two-dimensional scenarios.
• 📐 The second law of reflection is crucial: the angle of incidence (between the incident ray and the normal) is always equal to the angle of reflection (between the reflected ray and the normal).
• 🌟 If the angle of incidence is 0, the light ray is along the normal, and the angle of reflection will also be 0, causing the light to retrace its path.
• 🔄 For a convex mirror, parallel rays incident on the mirror reflect through the focus, and rays passing through the focus reflect parallel to the principal axis.
• 🎯 A ray through the center of curvature of a spherical mirror travels along the normal and reflects back along the same path, retracing its steps.
• 🖼️ When an object is placed outside the center of curvature of a concave mirror, its image is formed between the center of curvature (C) and the focus (F), and it's real, inverted, and diminished.
• 🤔 If an object is between the pole (P) and focus (F) of a concave mirror, the image is virtual, larger than the object, and cannot be captured on a screen.
• 🪞 For a convex mirror, all reflected rays diverge, and the image formed is virtual, diminished, and erect, appearing inside the mirror but cannot be projected onto a screen.
• 📌 The position and nature of the image depend on the object's placement relative to the mirror's focal points and curvature, with different outcomes for concave and convex mirrors.
• 🧭 Understanding the behavior of light rays as they interact with mirrors is essential for determining the location, size, and orientation of the image formed.

Q & A

What are the two main laws of reflection discussed in the script?

The first law of reflection is that the incident ray, the normal, and the reflected ray all lie in the same plane. The second law, which is more relevant to the discussion, states that the angle of incidence is always equal to the angle of reflection.

Why is the first law of reflection not useful for the discussion in the script?

The first law of reflection is not useful for the discussion because it applies to three-dimensional scenarios, and the script focuses on two-dimensional examples.

What does the angle of incidence represent in the context of the script?

The angle of incidence represents the angle between the incident ray and the normal to the mirror's surface at the point of incidence.

If the angle of incidence is 0, what happens to the reflected ray?

If the angle of incidence is 0, the ray of light is along the normal, and the angle of reflection will also be zero, causing the ray to go back along the normal, retracing its original path.

How can the position and nature of an image be determined using specific rays of light with a convex mirror?

By drawing specific rays of light such as those parallel to the principal axis, through the focus, through the center of curvature, and at the pole, one can determine the position and nature of the image formed by a convex mirror.

What is the definition of the focus in the context of mirrors?

The focus is the point through which all parallel rays of light converge after reflection from a mirror.

What type of image is formed when an object is placed outside the center of curvature of a concave mirror?

An inverted, real, and diminished image is formed when an object is placed outside the center of curvature of a concave mirror.

What happens to the image when an object is placed between the pole and the focus of a convex mirror?

When an object is placed between the pole and the focus of a convex mirror, the image formed is virtual, erect, and appears to be larger than the object.

Why are erect images considered virtual?

Erect images are considered virtual because they cannot be captured on a screen and only appear to diverge from a point behind the mirror.

How does the script explain the behavior of a ray of light aimed at the focus of a convex mirror?

The script explains that a ray of light aimed at the focus of a convex mirror will, after reflection, appear to go parallel to the principal axis.

What is the significance of the angle of incidence being equal to the angle of reflection?

The significance of the angle of incidence being equal to the angle of reflection is that it ensures the law of reflection is followed, which is crucial for determining the path of the reflected ray and the formation of images by mirrors.

Outlines

00:00

🔍 Laws of Reflection and Image Formation in Mirrors

This paragraph explains the laws of reflection and how they apply to the formation of images in mirrors. The first law, which states that the incident ray, the normal, and the reflected ray all lie in the same plane, is mentioned but deemed not useful for the discussion. The second law, which is crucial, states that the angle of incidence (the angle between the incident ray and the normal) is equal to the angle of reflection (the angle between the reflected ray and the normal). This law is used to predict the size, nature, and position of the image formed by a mirror. The paragraph then demonstrates how to use specific rays of light to determine the image's position for an object placed outside the center of curvature for a convex mirror. Four different rays are considered: one parallel to the principal axis, one passing through the focus, one through the center of curvature, and one directed at the pole. The analysis shows that the image is formed between the center of curvature and the focus, is diminished, inverted, and real, meaning it can be captured on a screen.

05:02

🔎 Image Formation with a Concave Mirror

The second paragraph discusses image formation with a concave mirror. It starts by considering the case where an object is placed between the principal axis and the focus (P and F). The paragraph outlines the process of drawing four specific rays of light to determine the image's position: a ray parallel to the principal axis that passes through the focus after reflection, a ray through the focus that becomes parallel after reflection, a ray through the center of curvature that retraces its path, and a ray directed at the pole that reflects with equal angles of incidence and reflection. The analysis reveals that the image is formed inside the mirror, is larger than the object, and is erect, indicating it is a virtual image that cannot be captured on a screen. The paragraph concludes by encouraging the viewer to practice drawing these rays to understand image formation with a concave mirror.

Keywords

💡Laws of Reflection

The laws of reflection are fundamental principles that govern how light behaves when it strikes a reflective surface. In the context of the video, the first law is mentioned but deemed not directly applicable to the discussion. The second law, however, is central to understanding image formation by mirrors. It states that the angle of incidence (the angle between the incident ray and the normal to the surface) is equal to the angle of reflection (the angle between the reflected ray and the normal). This law is crucial for predicting the path of light after it interacts with a mirror, as illustrated when discussing how rays of light are reflected by concave and convex mirrors.

💡Incident Ray

An incident ray is a ray of light that strikes a reflective or refractive surface. In the video, the behavior of the incident ray is essential for understanding the laws of reflection, particularly how it interacts with the normal at the point of incidence. The script explains that the incident ray, along with the normal and the reflected ray, must lie in the same plane, which is a fundamental concept for analyzing the reflection of light.

💡Normal

The normal is an imaginary line drawn perpendicular to the surface at the point where the incident ray strikes. It plays a critical role in the laws of reflection, as both the incident and reflected rays are related to it through their angles of incidence and reflection. The script uses the normal to explain how the angles of incidence and reflection are measured and how they are equal, which is vital for determining the path of the reflected light.

💡Angle of Incidence

The angle of incidence is the angle between the incident ray and the normal to the surface at the point of incidence. The video emphasizes that this angle is equal to the angle of reflection, which is a key principle in the laws of reflection. The script uses this concept to explain how changes in the angle of incidence result in corresponding changes in the angle of reflection, affecting the final direction of the reflected light.

💡Angle of Reflection

The angle of reflection is the angle between the reflected ray and the normal to the surface. According to the second law of reflection, which is central to the video's discussion, the angle of reflection is always equal to the angle of incidence. This principle is used to predict the direction in which light will be reflected after interacting with a mirror.

💡Convex Mirror

A convex mirror is a type of mirror with a curved surface that bulges outward. In the video, the properties of convex mirrors are discussed in the context of image formation. The script explains that when an object is placed in front of a convex mirror, the reflected rays appear to diverge from a point behind the mirror, creating a virtual, erect, and diminished image.

💡Concave Mirror

A concave mirror is a mirror with a curved surface that bends inward. The video script uses concave mirrors to demonstrate how they can form real, inverted, and magnified images. It explains that rays of light reflected from a concave mirror can be traced back to a single point, indicating where the image is formed, which is a key concept in understanding the reflective properties of concave mirrors.

💡Principal Axis

The principal axis is a line that passes through the center of curvature and the pole (the center point) of a spherical mirror. In the video, the principal axis is used as a reference for analyzing the paths of rays of light reflected by concave and convex mirrors. The script describes how rays parallel to the principal axis are crucial for determining the location and characteristics of the image formed by the mirror.

💡Focus

The focus is a point on the principal axis of a mirror where parallel rays of light converge after reflection from a concave mirror or appear to diverge from in the case of a convex mirror. The video script explains that rays parallel to the principal axis will pass through the focus after reflection, which is a key concept in understanding how concave mirrors form real images.

💡Virtual Image

A virtual image is an image that appears to be formed at a point from which the light rays do not actually diverge. In the video, virtual images are discussed in the context of convex mirrors, where the script explains that the image formed is erect and diminished but cannot be projected onto a screen, as it is not formed by actual light rays converging at a point.

💡Real Image

A real image is an image formed by the actual convergence of light rays and can be projected onto a screen. The video script contrasts real images with virtual images, explaining that real images are formed by concave mirrors when the object is placed outside the center of curvature. Real images are inverted and can be captured on a screen, as opposed to virtual images.

Highlights

Exploration of the laws of reflection, focusing on the second law which states that the angle of incidence equals the angle of reflection.

Explanation of how the angle of incidence and reflection affect the size of these angles.

Demonstration that if the angle of incidence is 0, the angle of reflection will also be 0, and the light will retrace its path.

Application of the laws of reflection to convex and concave mirrors to determine image size, nature, and position.

Use of specific rays of light to understand image formation, such as a ray parallel to the principal axis.

Definition of the focus as the point through which all parallel rays of light pass after reflection.

Discussion on how a ray passing through the focus will reflect to become parallel to the principal axis.

Illustration of how rays through the center of curvature reflect straight back, retracing their path.

Explanation that the image formed is between the center of curvature and the focus, and is real and inverted.

Case study of an object placed between the pole and the focus, leading to a virtual image inside the mirror.

Observation that virtual images are erect and larger than the object, and cannot be captured on a screen.

Application of the same ray tracing method to a convex mirror to determine the image's position.

Conclusion that for a convex mirror, parallel rays reflect as if coming from the focus, aiding in image location.

Description of how rays aimed at the focus reflect parallel to the principal axis after reflection.

Final case analysis with an object in front of a convex mirror, resulting in a diminished, erect virtual image.

Transcripts

so let's explore the laws of reflection

the first law says that the incident Ray

which is the ray that strikes the mirror

the normal which is a imaginary

perpendicular that you draw at that

point and the reflected ray all three

Rays lie in the same plane in this

example the plane is that of the

Blackboard now this rule is only useful

if you're dealing in three dimensions

but we're not dealing in three

dimensions so it's not useful for us so

don't worry too much about this law but

the second rule the second law which is

going to be important for us that rule

states that the angle of incidence which

is the angle between the incident Ray

and the normal not this angle but this

angle that will always equal the angle

of reflection the angle between the

reflected ray and the normal and what

this means is that if you have a larger

angle of reflection

angle of incidence you will have a long

larger angle of reflection if you have a

smaller angle of incidence smaller angle

of reflection and if the angle of

incidence is 0 which means the ray of

light is along the normal then the angle

of reflection will also be zero the ray

of light will go back along the normal

retracing its original path now let's

apply these two curve mirrors to find

the size nature and position of the

image so for example imagine we have an

object which is outside the center of

curvature for a convex concave mirror

where will its image be how do we figure

this out or we can draw a few specific

rays of light to help us out the first

ray of light we can draw is parallel to

the principal axis we know that this ray

of light after reflection has to go

through Focus why because that's the

definition of focus it's the point

through which all parallel rays of light

after reflection goes through

so that's the first ray of light I can

draw

then I can draw a ray of light that goes

through the focus if parallel rays of

light goes through the focus after

reflection then a ray of light goes

through the focus after reflection will

go parallel it's just the opposite of

that

and now by looking at these two

reflected Rays you can see that these

two reflected rays meet at this point

and so I know that the tip of the

object's image has to be formed here

and I can draw the image but before I do

that let me draw let me show you a few

other Rays I can draw as well a couple

of more another way I can draw is

through the center of curvature now if a

ray of light goes through the center of

curvature it is going along the normal

remember that normal for a spherical

mirror passes through the center of

curvature so this Ray is along the

normal and we just saw that any ray of

light goes in going along the normal

gets reflected straight back it retraces

the path

and so now this itself becomes the

reflected ray

and finally the fourth Ray that we can

draw is we can shoot array of light

right at the pole and then we know that

the principal axis this time which is

passing through the center of curvature

that acts as the normal and then we can

ensure that the reflected angle has the

same as the incident angle and we can

draw a reflected ray like this

and now you can see all the four

reflected ray pass through the common

point they all meet at one single point

and that is where our image is going to

be

and so we know now that the image is

between C and F it's going to be

diminished inverted and inverted images

are always real images these can be

captured on a screen

so we have solved our problem

okay consider a case where the object is

kept between P and F why don't you pause

and see if you can solve and figure out

where the image is going to be

okay now I'm not gonna draw all four

Rays that's not necessary

okay again one ray of light parallel to

the principal axis goes through the

focus

now the second ray of light where will I

draw I can't draw through the focus

because I know it's not going to hit the

mirror I can't draw through the center

of curvature because that's also not

going to hit the mirror so I'm going to

directly draw the fourth Ray which is

I'm going to shoot it right at the pole

this snap becomes a normal this is the

angle of incidence and then the angle of

reflection has to be equal to the angle

of reflection incidence and then this

becomes the reflected array

and now these are the two reflected

arrays where do they meet notice they

will not meet anywhere which means I

will not get an image on this side

so if I don't see them meeting this side

I will retrace them back and notice they

do meet here which means it appears that

these two rays are coming from here

they're not really but it appears like

that and so now the tip of the objects

uh image is going to be over here

and so this is where the image is going

to be it's inside the mirror

the image is bigger than the object and

you can see the image is erect which

means it's a virtual image virtual

meaning you cannot capture it on a

screen all erect images are virtual

images you can't capture them on a

screen okay one last case you have an

object in front of a convex mirror where

will the image be again try to draw all

the four rays of light that we saw which

we drew for the concave mirror

okay let's do this this might sound a

little tricky but let's do this first

Way of Light I'm gonna pass parallel to

the principal axis where does it go it

doesn't go through the focus because

this is a mirror and it can't go inside

the mirror instead it reflects as if it

appears to come from the focus

can you see that it's very similar to

what we drew earlier parallel trees of

light reflects appearing to come from

the focus

that's the first three

next I'm going to draw array of light

that is aimed at the focus

if a ray of light is aimed at the focus

after reflection it will go parallel to

the principal axis

just like before parallel goes

just like before if the incident Ray is

parallel the reflected ray appears to

come from the focus

and so if the incident Ray is towards

the focus the reflected ray becomes

parallel to the principal axis these two

rays are enough for me to figure out

where the image is going to be but I'm

going to draw a few more Rays the next

thing I'm going to draw is aiming at the

center of curvature

now I know that this is along the normal

which means the reflected ray will

retrace its path it will go along the

same path

and the fourth ray of light I can hit at

the pole making sure that the angle of

incidence and the angle of reflection is

exactly equal and that gives me the

reflected array and again I have these

four rays of light

and where will the image be notice all

the four rays of light appear to be

going away from each other which means

they are not going to meet anywhere so I

have to retrace them back and if I

retrace all of them back look they

appear to be coming from one single

point

so I know that the tip of these objects

here image is going to be somewhere over

here and therefore I'm gonna get the

image here notice it's inside the mirror

between P and F it is diminished smaller

than the object and it is erect which

means it's a virtual image it cannot be

captured on a screen