Geometrical Optics – Page 2

Triangle on a concave mirror

January 28th, 2022jeefirst0 Comments

JEE Advanced 2018 Paper 2, Question 4

A wire is bent in the shape of a right angled triangle and is placed in front of a concave mirror of focal length $f$ , as shown in the figure. Which of the figures shown in the four options qualitatively represent(s) the shape of the image of the bent wire? (These figures are not to scale.)

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Related article: Optics without ray diagrams: Mirrors

Solution

If the object is kept between a concave mirror and its focal point the image is virtual and upright (see this note). Recall that an object at a distance …

Optics without ray diagrams: Mirrors

January 27th, 2022jeefirst0 Comments

The usual discussions of geometrical optics often rely too heavily on ray diagrams to locate the image and study its properties. We will demonstrate that all of these insights can be obtained purely by algebra on the mirror equation. Developing these instincts will help us solve optics problems without having to use crude, hand drawn, and often inaccurate ray diagrams. Our main results are summarized in the table below.

We begin by recalling the mirror equation

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

where $p$ and $q$ the distances of the object and image from the mirror, and the focal length $f=R/2$ , for a spherical mirror with …

Three glass cylinders

January 24th, 2022jeefirst0 Comments

JEE Advanced 2019 Paper 2, Question 6

Three glass cylinders of equal height $H=30 \, {\rm cm}$ and same refractive index $n=1.5$ 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 ( $R=3 \, {\rm m}$ ). If $H_{1}, H_{2}$ , and $H_{3}$ are the apparent depths of a point $X$ on the bottom of the three cylinders, respectively, the correct statement(s) is/are:

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$H_{2}>H_{1}$
$H_{3}>H_{1}$
$H_{2}>H_{3}$
$0.8 \, {\rm cm} < (H_{2}-H_{1}) < 0.9 \, {\rm cm}$

Solution

We can get some intuition for what happens in each case by drawing some simple ray diagrams, as …

Total internal reflection from a prism

January 20th, 2022jeefirst0 Comments

JEE Advanced 2019 Paper 2, Question 11

A monochromatic light is incident from air on a refracting surface of a prism of angle $75^{\circ}$ and refractive index $n_{0}=\sqrt{3}$ . The other refracting surface of the prism is coated by a thin film of material of refractive index $n$ as shown in figure. The light suffers total internal reflection at the coated prism surface for an incidence angle of $\theta \leq 60^{\circ}$ . What is the value of $n^{2}$ ?

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Solution

First we trace the given incident ray through the prism to find the angle at which it is incident on the opposite face (see figure below). For …

Delay in a fiber optic cable

January 9th, 2022jeefirst0 Comments

JEE Advanced 2019 Paper 1, Question 18

A planar structure of length $L$ and width $W$ is made of two different optical media of refractive indices $n_{1}=1.5$ and $n_{2}=1.44$ as shown in figure. If $L \gg W$ , a ray entering from end ${\rm AB}$ will emerge from end ${\rm CD}$ only if the total internal reflection condition is met inside the structure. For $L=9.6$ m, if the incident angle $\theta$ is varied, the maximum time taken by a ray to exit the plane $\mathrm{CD}$ is $t \times 10^{-9}$ s. Determine $t$ .

[ Speed of light $c=3 \times 10^{8}$ m/s. ]

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Solution

To ensure that the ray spends the maximum possible time inside the media, we should arrange it so …