1

JEE Main 2019 (Online) 11th January Morning Slot

An object is at a distance of 20 m from a convex lens of focal length 0.3 m. The lens forms an image of the object. If the object moves away from the lens at a speed of 5 m/s, the speed and direction of the image will be :
A
1.16 $\times$ 10–3 m/s towards the lens
B
2.26 $\times$ 10–3 m/s away from the lens
C
3.22 × 10–3 m/s towards the lens
D
0.92 $\times$ 10$-$3 m/s away from the lens

Explanation

From lens equation

${1 \over v} - {1 \over u} = {1 \over f}$

${1 \over v} - {1 \over {\left( { - 20} \right)}} = {1 \over {\left( {.3} \right)}} = {{10} \over 3}$

${1 \over v} = {{10} \over 3} - {1 \over {20}}$

${1 \over v} = {{197} \over {60}};v = {{60} \over {197}}$

m = $\left( {{v \over u}} \right)$ = ${{\left( {{{60} \over {197}}} \right)} \over {20}}$

velocity of image wrt. to lens is given by

vI/L = m2vO/L

direction of velocity of image is same as that of object

vO/L = 5 m/s
2

JEE Main 2019 (Online) 11th January Morning Slot

The variation of refractive index of a crown glass thin prism with wavelength of the incident light is shown. Which of the following graphs is the correct one, if Dm is the angle of minimum deviation?

A
B
C
D

Explanation

Since Dm = ($\mu$ $-$ 1) A & on increasing the wavelength, $\mu$ decreases & hence Dm decreases.
3

JEE Main 2019 (Online) 11th January Evening Slot

In a double-slit experiment, green light (5303$\mathop A\limits^ \circ$) falls on a double slit having a separation of 19.44 $\mu$m and awidht of 4.05 $\mu$m. The number of bright fringes between the first and the second diffraction minima is :
A
04
B
05
C
10
D
09

Explanation

For diffraction

location of 1st minime

y1 = ${{D\lambda } \over a}$ = 0.2469 D$\lambda$

location of 2nd minima

y2 = ${{2D\lambda } \over a}$ = 0.4938 D$\lambda$

Now for interference

Path difference at P.

${{dy} \over D}$ = 4.8$\lambda$

path difference at Q

${{dy} \over D}$ = 9.6$\lambda$

So orders of maxima in between P & Q is 5, 6, 7, 8, 9

So 5 bright fringes all present between P & Q.
4

JEE Main 2019 (Online) 11th January Evening Slot

A monochromatic light is incident at a certain angle on an equilateral triangular prism and suffers minimum deviation. If the refractive index of the material of the prism is $\sqrt 3$, then the angle of incidence is:
A
60o
B
45o
C
90o
D
30o

Explanation

i = e

r1 = r2 = ${A \over 2}$ = 30o

by Snell's law

1 $\times$ sin i = $\sqrt 3 \times {1 \over 2} = {{\sqrt 3 } \over 2}$

i = 60