Refractive Index

- Assertion (A): The refractive index of a material is the ratio of the speed of light in vacuum to the speed of light in the material. Since the speed of light in glass is slower than that in air, the refractive index of glass is indeed more than that of air. Hence, assertion (A) is true.
- Reason (R): The optical density of a medium is not directly related to its mass density. The refractive index (which determines optical density) is related to the speed of light in the material, while mass density relates to the mass per unit volume of the material. Therefore, reason (R) is false. Since (A) is true and (R) is false, the correct answer is (2) "Assertion (A) is true but (R) is false."

Step 1: The focal length of a lens in different media is given by: In air: In water:

Step 2: Using the lens maker's formula, the focal length in water is related to the focal length in air by the refractive index ratio: Substitute the values: Thus, the focal length changes to 96 cm.

Concept: Refractive index of a prism at minimum deviation: where = angle of prism = minimum deviation. Step 1: {Identify the prism angle.} For an equilateral prism: Given Step 2: {Substitute in formula.} Thus the refractive index is approximately

Step 1: Understanding the given information.
The lens is a convex lens, and sunlight is focused on a paper, causing it to burn when the lens is at a specific distance (30 cm) from the paper. The radius of curvature of the lens is given as 60 cm. The distance at which the paper starts burning corresponds to the focal length of the lens, and the focal length of a convex lens is related to the radius of curvature by the formula: Substituting the value of : Thus, the focal length of the lens is 30 cm, which matches the distance from the lens to the paper.
Step 2: Using the lens formula.
The lens formula relates the focal length , the object distance , and the image distance as: In this case, the object is at infinity (as sunlight is parallel), and the image is formed at the focal point of the lens. Therefore, the image distance is equal to the focal length . So, we have: Since the object distance is at infinity, the equation simplifies to:
Step 3: Refractive index calculation.
The refractive index of the lens material is related to the focal length and the radius of curvature by the formula: Substituting the known values and : Simplifying the equation: Thus, we get: The refractive index of the lens is 2. Now, since the refractive index is given as , we equate: Thus, the value of is:

Step 1: Understanding the Concept:
The focal length of a lens depends on the refractive index of its material and the radii of curvature of its two surfaces. This relationship is described by the Lens Maker's Formula. For a biconvex lens, the first surface has a positive radius of curvature and the second has a negative radius of curvature.

Step 2: Key Formula or Approach:
Lens Maker's Formula:
For an equiconvex lens: and .

Step 3: Detailed Explanation:
Given the refractive index .
Using the sign convention for a biconvex lens with equal radii:




Taking the reciprocal to find the focal length :

The required ratio of focal length to radius of curvature is:


Step 4: Final Answer:
The ratio of its focal length and radius of curvature is 1.25.