January 2022 – JEE First

Sliding on a block with a circular cut

January 30th, 2022jeefirst0 Comments

JEE Advanced 2017 Paper 1, Question 2

A block of mass $M$ has a circular cut with a frictionless surface as shown. The block rests on the horizontal frictionless surface of a fixed table. Initially the right edge of the block is at $x=0$ , in a co-ordinate system fixed to the table. A point mass $m$ is released from rest at the topmost point of the path as shown and it slides down. When the mass loses contact with the block, its position is $x$ and the velocity is $v$ . At that instant, which of the following options is/are correct?

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The position

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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 …

Oblique beam on a double slit

January 22nd, 2022jeefirst0 Comments

JEE Advanced 2019 Paper 2, Question 7

In a Young’s double slit experiment, the slit separation $d$ is 0.3 mm and the screen distance $D$ is 1 m. A parallel beam of light of wavelength 600 nm is incident on the slits at angle $\alpha$ as shown in figure. On the screen, the point $O$ is equidistant from the slits and distance $P O$ is 11.0 mm. Which of the following statement(s) is/are correct?

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For $\alpha=\frac{0.36}{\pi}$ degree, there will be destructive interference at point $O$ .
For $\alpha=0$ , there will be constructive interference at point $P$ .
For $\alpha=\frac{0.36}{\pi}$ degree, there will be destructive interference at point $P$ .
Fringe spacing

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