Question

1. The second order fringe when 700 nm light falls on a double slit is
observed at a 15° angle to the initial beam direction. How far apart are
the slits? Ans: 5.41 x 10^-6 m

2. Light of frequency 6 x 10^14 Hz falls on a pair of slits that are 0.0002 cm
apart. The center of the slits is 50 cm from the screen. How far from the
central bright line will the first order line appear? Ans: 0.13 m

3. Monochromatic light falling on two slits 0.026 mm apart produces the
fourth-order line at a 6.4°angle. What is the wavelength of light used?
Ans: 7.25 x 10^-7 m

4. Light of wavelength 6.5 x 10^-5 cm passes through a single slit and falls on
a screen 100 cm away. The third-order dark band is 0.25 cm from the
center of the pattern. What is the slit width? Ans: 7.8 x 10^- 4 m

5. A diffraction grating with 760 lines per cm is used to form a diffraction
pattern. The first-order line is 3 cm from the central bright spot. The screen
is 80 cm away. What is the wavelength of light used? Ans: 4.93 x 10^-7 m

6. At what angle will 710 nm light produce a third order maximum when
falling on a grating whose slits are 0.0017 cm apart? Ans: 7.2°

Answer 1

1.

Since in double slit ,

Path difference = dx = d*sin() = n*

for second order, n = 2

given, = 700 nm = 7*10^-7 m

= 15 deg

So, difference between slits = d = n*/sin

d = 2*(7*10^-7)/sin(15 deg)

d = 5.41*10^-6 m

2.

Given frequency of light = meu = c/ = 6*10^14 Hz

So, = (3*10^8)/(6*10^14) = 5*10^-7

= 500 nm

distance for first order line is given by,

y = n**D/d

here, n = 1

D = 50 cm

d = 0.0002 cm

So, y = 1*(5*10^-7)*50/0.0002

y = 0.13 m

3.

In double slit ,

Path difference = dx = d*sin() = n*

for fourth order, n = 4

given, = 6.4 deg

difference between slits = d = 0.026 mm = 2.6*10^-5 m

So, wavelength = = d*sin()/n

= (2.6*10^-5)*sin(6.4 deg)/4

= 7.25*10^-7 m

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