Q. 60

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Found in: Page 958

### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

Book edition 4th
Author(s) Randall D. Knight
Pages 1240 pages
ISBN 9780133942651

# Scientists shine a laser beam on a -wide slit and produce a diffraction pattern on a screen behind the slit. Careful measurements show that the intensity first falls to of maximum at a distance of from the center of the diffraction pattern. What is the wavelength of the laser light?Hint: Use the trial-and-error technique demonstrated in Example to solve the transcendental equation.

Wavelength of the laser light is .

See the step by step solution

## Step 1: Calculation for intensity

Intensity is ,

Where,

The maximum intensity is ,

Width of the slit is ,

The wavelength is

And the distance between the slit and the screen is .

Rearrange the solution above.

The intensity decreases to of the high capacity.

So,

## Step 2: Calculation for

Use the trial-and-error method as outlined in the textbook's example.

Let .

So,

The first minimum

This amount is lower than the solution. Because the intensity has tapered off more in this case, we should take our first forecast higher than the one given in the example.

For second trial, ,

So,

For third trial,

So,

## Step 3: Calculation for wavelength

Average of the value is,

So,

Wavelength is,