How To Use LENS MAKER FORMULA : Sign Convention and LENS NUMERICALS: Class X :ICSE /CBSE PHYSICS

Summary

The video script offers a detailed explanation of the lens maker formula, crucial for determining image positions in lenses. It emphasizes four key rules: a convex lens has a positive focal length, a concave lens has a negative one; all distances are measured from the optical center; distances in the direction of incident light are positive; and heights above the principal axis are positive. A practical example demonstrates applying these rules to find the image position for a convex lens with a 10 cm focal length and an object placed 20 cm away, resulting in an image 20 cm from the optical center on the positive side.

Takeaways

• 🔍 The Lens Maker Formula is given by 1/f = 1/V - 1/U, where f is the focal length, V is the image distance, and U is the object distance.
• 🌟 For a convex lens, the focal length (f) is always positive, while for a concave lens, it is always negative.
• 📏 All distances, whether object or image distance, are measured from the optical center of the lens.
• 📍 The direction of the incident light determines the positive direction for distance measurements in lens problems.
• 📈 Heights measured above the principal axis are considered positive, while those below are negative.
• 📚 Understanding the four rules is essential for solving any lens-related problem using the Lens Maker Formula.
• 🔄 The formula is used to find the position of the image formed by lenses when the object is placed at different positions.
• 👉 In the example given, a convex lens with a focal length of 10 cm is used, and the object is placed 20 cm from the lens.
• ➡️ The object distance (U) is considered negative in the formula because it is in the positive direction from the optical center.
• 🔢 By applying the Lens Maker Formula, the image distance (V) is calculated to be 20 cm from the optical center in the positive direction.
• 🖼️ The image is formed at the same distance from the lens as the object but on the opposite side, indicating a real image.

Q & A

What is the lens maker formula?

The lens maker formula is given by 1/f = 1/v - 1/u, where 'f' is the focal length of the lens, 'v' is the image distance, and 'u' is the object distance.

What is the significance of the lens maker formula in optics?

The lens maker formula is used to determine the position of the image formed by a lens when an object is placed at different positions relative to the lens.

What are the two types of lenses mentioned in the script, and how do they form images differently?

The two types of lenses mentioned are convex and concave lenses. Convex lenses converge light and typically form real, inverted images, while concave lenses diverge light and usually form virtual, upright images.

Why is the sign of the focal length important in the lens maker formula?

The sign of the focal length is crucial as it indicates the type of lens: a positive sign for a convex lens and a negative sign for a concave lens, which affects the calculation of image positions.

What are the four rules for applying the lens maker formula as outlined in the script?

The four rules are: 1) The focal length of a convex lens is always positive, and for a concave lens, it is always negative. 2) All distances are measured from the optical center. 3) Distances measured in the direction of incident light are positive. 4) Heights above the principal axis are positive, while those below are negative.

Why is the optical center important when measuring distances in the lens maker formula?

The optical center is the reference point from which all distances (object distance 'u' and image distance 'v') are measured in the lens maker formula, ensuring consistency and accuracy in calculations.

How does the direction of incident light affect the calculation of distances in the lens maker formula?

The direction of incident light determines the positive direction for distance measurements. Distances measured in the direction of the incident light are considered positive, while those in the opposite direction are negative.

What does the principal axis represent in the context of the lens maker formula?

The principal axis is a reference line that passes through the optical center of the lens. Heights above this axis are considered positive, while those below are negative in the lens maker formula.

Can you provide an example of how to use the lens maker formula with a convex lens?

Sure. Given a convex lens with a focal length of 10 cm and an object placed 20 cm from the lens, you would use the formula 1/f = 1/v - 1/u, where f = 10 cm (positive), u = -20 cm (negative because the object is in the positive direction), and solve for 'v' to find the image distance.

What is the image distance if a convex lens with a 10 cm focal length is used and the object is placed 20 cm from the lens?

Following the rules and applying the lens maker formula, the image distance 'v' would be calculated as 20 cm in the positive direction, meaning the image is formed 20 cm from the optical center on the same side as the object.

How does the height above or below the principal axis affect the calculation in the lens maker formula?

Heights measured above the principal axis are considered positive, while those below are negative. This is important for calculating the position of the image, especially when the object is not aligned with the principal axis.