JEE Advanced 2017 Paper 1, Question 10
A monochromatic light is traveling in a medium of refractive index 
. It enters a stack of glass layers from the bottom side at an angle 
. The interfaces of the glass layers are parallel to each other. The refractive indices of different glass layers are monotonically decreasing as 
, where 
is the refractive index of the 
slab and 
(see the figure). The ray is refracted out parallel to the interface between the 
and slabs from the right side of the stack. What is the value of 
?
Solution
Consider the trajectory of …
and same refractive index 
are placed on a horizontal surface as shown in figure. Cylinder I has a flat top, cylinder II has a convex top and cylinder III has a concave top. The radii of curvature of the two curved tops are same (
). If 
, and 
are the apparent depths of a point 
on the bottom of the three cylinders, respectively, the correct statement(s) is/are:
and refractive index 
. The other refracting surface of the prism is coated by a thin film of material of refractive index 
as shown in figure. The light suffers total internal reflection at the coated prism surface for an incidence angle of 
. What is the value of 
?
and width 
is made of two different optical media of refractive indices 
and 
as shown in figure. If 
, a ray entering from end 
will emerge from end 
only if the total internal reflection condition is met inside the structure. For 
m, if the incident angle 
is varied, the maximum time taken by a ray to exit the plane 
is 
s. Determine 
.
m/s. ]