1

### JEE Main 2019 (Online) 11th January Morning Slot

In a Young's double slit experiment, the path difference, at a certain point on the screen, between two interfering waves is ${1 \over 8}$ th of wavelength. The ratio of the intensity at this point to that at the centre of a bright fringe is close to :
A
0.94
B
0.85
C
0.74
D
0.80

## Explanation

$\Delta$x $=$ ${\lambda \over 8}$

$\Delta$$\phi$ $=$ ${{\left( {2\pi } \right)} \over \lambda }{\lambda \over 8} = {\pi \over 4}$

I $=$ I0cos2$\left( {{\pi \over 8}} \right)$

${{\rm I} \over {{{\rm I}_0}}} =$ cos2$\left( {{\pi \over 8}} \right)$
2

### 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
3

### 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.
4

### 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.