A beam of light of  = 600 nm from a distant source falls on a single slit 1 mm wide and the resulting diffraction pattern is observed on a screen 2 m away. The distance between first dark fringes on either side of the central bright fringe is,

• 1.2 cm

• 1.2 mm

• 2.4 cm

• 2.4 mm

D.

2.4 mm

From the above figure,

For small  and when  is counted in rad, tan 

So, 

A boy is trying to start a fire by focusing sunlight on a piece of paper using an equal convex lens of focal length 10 cm. The diameter of the sun is 1.39 x 10⁹ m  and its mean distance from the earth is 1.5 x 10¹¹ m. What is the diameter of the sun's image on the paper?

• 9.2 x 10^-4 m

• 6.5 x 10^-4 m

• 6.5 x 10^-5 m

• 12.4 x 10^-4 m

A parallel beam of fast moving electrons is incident normally on a narrow slit. A fluorescent screen is placed at a large distance from the slit. If the speed of the electrons is increased, then which of the following statements is correct ?

• Diffraction pattern is not observed on the screen in the case of electrons.

• The angular width of the central maximum of the diffraction pattern will increase

• The angular width of the central maximum will decrease

• The angular width of the central maximum will be unaffected

A siren emitting a sound of frequency 800 Hz moves away from an observer towards a cliff at a speed of 15 m/s. Then, the frequency of sound that the observer hears in the echo reflected from the cliff is (Take, velocity of sound in air = 330 m/s)

• 800 Hz

• 838 Hz

• 885 Hz

• 765 Hz

B.

838 Hz

The situation can be illustrated as follows:

Frequency of sound that the observer hear in the echo reflected from the cliff is given by,
f' = 

where,
f = original frequency of source
v= velocity of the sound
v_s = velocity of the source
So, 

For a parallel beam of monochromatic light of wavelength 'λ'diffraction is produced by single slit whose width 'a' is of the order of the wavelength of the light. If 'D' is the distance of the screen from the slit the width of the central maxima will be

• 2Dλ/a

• Dλ/a

• Da/λ

• 2Da/λ