Progressive refraction through glass layers

JEE Advanced 2017 Paper 1, Question 10

A monochromatic light is traveling in a medium of refractive index n=1.6. It enters a stack of glass layers from the bottom side at an angle \theta=30^{\circ}. The interfaces of the glass layers are parallel to each other. The refractive indices of different glass layers are monotonically decreasing as n_{m}=n-m \Delta n, where n_{m} is the refractive index of the m^{\rm th} slab and \Delta n=0.1 (see the figure). The ray is refracted out parallel to the interface between the (m-1)^{\rm th} and m^{\rm th} slabs from the right side of the stack. What is the value of m?

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Consider the trajectory of …

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Convex lens with two materials

JEE Advanced 2019 Paper 1, Question 10

A thin convex lens is made of two materials with refractive indices n_1 and n_2 as shown in figure. The radius of curvature of the left and right spherical surfaces are equal. f is the focal length of the lens when n_1 = n_2 = n. The focal length is f + \Delta f when n_1 = n and n_2 = n + \Delta n. Assuming \Delta n \ll (n-1) and 1 < n < 2, the correct statement(s) is/are,

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  1. \bigg| \frac{\Delta f}{f} \bigg| < \bigg| \frac{\Delta n}{n} \bigg|
  2. For n=1.5, \Delta n = 10^{-3} and f = 20 cm, the value of |\Delta f| will be 0.02 cm (round off to 2^{\rm nd} decimal place).
  3. If \frac{\Delta n}{n} < 0 then \frac{\Delta f}{f} > 0
  4. The relation between \frac{\Delta f}{f} and \frac{\Delta n}{n} remains unchanged if both the convex surfaces are replaced by concave surfaces of the same radius of curvature.


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