Refracting surface with a coating

JEE Advanced 2014 Paper 1, Question 9

A transparent thin film of uniform thickness and refractive index n_{1}=1.4 is coated on the convex spherical surface of radius R at one end of a long solid glass cylinder of refractive index n_{2}=1.5, as shown in the figure. Rays of light parallel to the axis of the cylinder traversing through the film from air to glass get focused at distance f_{1} from the film, while rays of light traversing from glass to air get focused at distance f_{2} from the film. Then

Rendered by

  1. \left|f_{1}\right|=3 R
  2. \left|f_{1}\right|=2.8 R
  3. \left|f_{2}\right|=2 R
  4. \left|f_{2}\right|=1.4 R

Related Problem: Lensing by oil on water


We can solve this problem using …

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Lenses II: Image formation

Continuing our discussion from the previous chapter, we can use the thin lens equation and our knowledge of the signs of f, to determine the position, orientation, and magnification of the image for different object distances p. This is similar to the analysis we did for mirrors here. The results are summarized in the table below.

Converging lens

The focal length of a converging lens is positive. That means light from infinity will be brought to focus behind the lens. We will begin our analysis there.

Starting from p = \infty

Consider an object kept in front of a converging lens. …

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Lenses I: The thin lens equation

A lens is a refracting element with two curved surfaces. Light changes direction as it refracts through each of these surfaces. If the thickness of the lens is small compared to the radius of curvature of each surface, we can think of light as bending just once at the central plane of the lens. This approximation is justified more rigorously in chapter 27 of the Feynman lectures. For our present discussion we start with equation (27.12) from that book, called the thin lens equation,

(1)   \begin{equation*}   \frac{1}{p} + \frac{1}{q} = \frac{1}{f} ,  \end{equation*}

where p is the object distance from the lens, q is the image distance, and …

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