Geometrical Optics – JEE First

Refracting surface with a coating

June 7th, 2022jeefirst0 Comments

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

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

Related Problem: Lensing by oil on water

Solution

We can solve this problem using …

Lensing by oil on water

May 23rd, 2022jeefirst0 Comments

JEE Advanced 2011 Paper 2, Question 36

Water (with refractive index $=\frac{4}{3}$ ) in a tank is $18 \mathrm{~cm}$ deep. Oil of refractive index $\frac{7}{4}$ lies on water making a convex surface of radius of curvature $R=6 {\rm ~cm}$ as shown. Consider oil to act as a thin lens. An object ‘ $S$ ’ is placed $24 \mathrm{~cm}$ above water surface. The location of its image is at ‘ $x$ ’ cm above the bottom of the tank. What is ‘ $x$ ’?

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Solution

To find the location of the final image we consider the oil and the water in the tank as a combination of two elements: a lens and a …

Lenses II: Image formation

May 15th, 2022jeefirst0 Comments

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. …

Lenses I: The thin lens equation

May 14th, 2022jeefirst0 Comments

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 …

Progressive refraction through glass layers

March 4th, 2022jeefirst0 Comments

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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Solution

Consider the trajectory of …