1
MCQ (Single Correct Answer)

JEE Main 2017 (Online) 8th April Morning Slot

A single slit of width b is illuminated by a coherent monochromatic light of wavelength $$\lambda $$. If the second and fourthminima in the diffraction pattern at a distance 1 m from the slit are at 3 cm and 6 cm respectively from the central maximum, what is the width of the central maximum ? (i.e. distance between first minimum on either side of the central maximum)
A
1.5 cm
B
3.0 cm
C
4.5 cm
D
6.0 cm

Explanation

For single slit diffraction, sin$$\theta $$ = $${{n\lambda } \over b}$$

From central maxima the position of nth minima = $${{n\lambda D} \over b}$$

Now when,

n = 2, then x2 = $${{2\lambda D} \over b}$$ = 0.03 . . . .(1)

n = 4, then x4 = $${{4\lambda D} \over b}$$ = 0.06 . . . .(2)

Performing (2) $$-$$ (1) we get,

x4 $$-$$ x2 = $${{2\lambda D} \over b}$$ = 0.03

$$\therefore\,\,\,$$ $${{\lambda D} \over b}$$ = $${{0.03} \over 2}$$

As, width of crntral maximum

= $${{2\lambda D} \over b}$$

= 2 $$ \times $$ $${{0.03} \over 2}$$

= 0.03 m

= 3 cm
2
MCQ (Single Correct Answer)

JEE Main 2017 (Online) 9th April Morning Slot

A single slit of width 0.1 mm is illuminated by a parallel beam of light of wavelength 6000 $$\mathop A\limits^ \circ $$ and diffraction bands are observed on a screen 0.5 m from the slit. The distance of the third dark band from the central bright band is :
A
3 mm
B
9 mm
C
4.5 mm
D
1.5 mm
3
MCQ (Single Correct Answer)

JEE Main 2018 (Offline)

The angular width of the central maximum in a single slit diffraction pattern is 60°. The width of the slit is 1 $$\mu $$m. The slit is illuminated by monochromatic plane waves. If another slit of same width is made near it, Young’s fringes can be observed on a screen placed at a distance 50 cm from the slits. If the observed fringe width is 1 cm, what is slit separation distance? (i.e. distance between the centres of each slit.)
A
100 $$\mu $$m
B
25 $$\mu $$m
C
50 $$\mu $$m
D
75 $$\mu $$m

Explanation



Given 2$$\theta $$ = 60o

$$ \Rightarrow $$ $$\theta $$ = 30o

We know,

$$a$$ sin $$\theta $$ = n $$\lambda $$

for first minima n = 1,

$$\therefore\,\,\,$$ At first minima

$$a$$ sin = $$\lambda $$

$$ \Rightarrow $$$$\,\,\,$$ 10$$-$$6 $$ \times $$ sin 30o = $$\lambda $$

$$ \Rightarrow $$$$\,\,\,$$ $$\lambda $$ = $${{{{10}^{ - 6}}} \over 2}$$ m

Now after making a new slit,

$$\therefore\,\,\,$$ Fringe width, $$\beta $$ = $${{\lambda D} \over d}$$

given, D = 50 cm and $$\beta $$ = 1 cm.

$$\therefore\,\,\,$$ 1 $$ \times $$ 10$$-$$2 = $${{0.5 \times {{10}^{ - 6}} \times 50 \times {{10}^{ - 2}}} \over d}$$

$$ \Rightarrow $$$$\,\,\,$$ d = 25 $$ \times $$ 10$$-$$6 m = 25 $$\mu $$m.
4
MCQ (Single Correct Answer)

JEE Main 2018 (Offline)

Unpolarized light of intensity I passes through an ideal polarizer A. Another identical polarizer B is placed behind A. The intensity of light beyond B is found to be I/2. Now another identical polarizer C is placed between A and B. The intensity beyond B is now found to be I/8. The angle between polarizer A and C is :
A
60o
B
30o
C
45o
D
0o

Explanation



As after B intensity of light does not drops, it means both A and B are alligned in single line means their plane of polarization is same.



Let C makes an angle $$\theta $$ with A then C will make $$\theta $$ with B also, as both A and B are alligned in a single line.

So, after C intensity is = $${{\rm I} \over 2}$$ cos2$$\theta $$ , and , intensity after B = $${{\rm I} \over 2}$$ cos2$$\theta $$ $$ \times $$ cos2$$\theta $$

   According to question,

$${{\rm I} \over 2}$$ cos4$$\theta $$ = $${{\rm I} \over 8}$$

$$ \Rightarrow $$\,\,\, CO4$$\theta $$ = $${{\rm I} \over 4}$$

$$ \Rightarrow $$$$\,\,\,$$ cos$$\theta $$ = $$ = {1 \over {\sqrt 2 }}$$ = cos45o

$$\therefore\,\,\,$$ $$\theta $$ = 45o

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