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College Physics (Urone)
Found in: Page 997

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Short Answer

How many lines per centimeter are there on a diffraction grating that gives a first-order maximum for 470nm blue light at an angle of 25.0?

The lines per cm for the first-order maximum are 8929 per centimeter.

See the step by step solution

Step by Step Solution

Step 1: Given data

λ=470 nm109 m1 nm=4.70 , 107 m

The wavelength of the blue light is

The order of maximum is 1.

The angle at which the first-order maximum is observed 25.0

Step 2: Evaluating the lines per centimeter for first-order maximum

The equation of the constructive interference can be expressed as

d sinθ= …………………(1)

Where, d , λ , θ and m is the separation between slits, the wavelength of the incident light, and the angle made with the maximum and order of maximum, respectively.

Therefore, if we substitute the given data in equation (1) for m=1, we will get,

We then evaluate the number of lines per centimeter, n, using the relation:

n=1.0 cmd.

Substitute the value in the above expression, and we get,

n=1.0 cm1.12×106 m1 m100 cm 8929

Therefore, the lines for the first-order maximum are 8929 per centimeter.

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