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Monochromatic light falls on two very narrow slits 0.048 mm apart. Successive fringes on a screen...

Monochromatic light falls on two very narrow slits 0.048 mm apart. Successive fringes on a screen 6.00 m away are 8.5 cm apart near the center of the pattern. Determine the wavelength and frequency of the light.
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Answer #1
Concepts and reason

The concepts used to solve this problem are diffraction, double slit interference, wavelength and frequency.

Use the expression for slit separation, distance between the slit and screen, fringe separation to find the wavelength.

Use the relation between frequency, wavelength and speed of light to find the frequency.

Fundamentals

Interference is a physical occurrence in which two waves superpose to form a resultant wave of greater, lower or same amplitude.

The expression for two slit interference,

Here, the slit separation distance is, the distance between screen and the slit is , the fringe separation is and the wavelength of the incident light is .

The two slit interference expression is,

ya

Rearrange the expression to get .

Substitute 8.5cm
for , 0.048 mm
for and 6.00 m
for .

(8.5cm)(cro.com (0.048mm) 10m
1 mm
1=-
6.00m
= 0.68x10m

The expression relating of wavelength, frequency and speed of light is,

Iv=c

Rearrange the above expression to get the frequency.

Substitute 3x108 m/s
for and 0.68x10m
for .

V
3x108 m/s
=
0.68x10m
= 4.41x104 Hz

Ans:

The wavelength of the light is0.68x106m
.

The frequency of the light is 4.41 x 1014 Hz
.

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