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Q. 43

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 956

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Illustration

Short Answer

A diffraction grating with is illuminated with light of wavelength . A very wide viewing screen is behind the grating.
What is the distance between the two bright fringes? How many bright fringes can be seen on the screen?

Part

The bright fringe's distance is

Part

The number of bright fringes on screen is

See the step by step solution

Step by Step Solution

Step: 1 Finding the distance: (part a)

To begin, remember that we won't utilise the little angle approximation in optical device issues since the angle in these situations is never small. Now we must determine the gap between the two brilliant fringes, each of which is on the other side of the centre bright fringe. We'll measure the space between the two fringes, and also the spacing between the two fringes are double that measurement "(due to symmetry)". the shape of the standards for colorful fringes is

is what we've been looking for. Thus

Given that the optical device contains , the space between any two successive slits is

Step: 2 Finding the intense fringe distance: (part a)

We can use the subsequent relationship to compute the space of the primary bright fringe from the centre maximum now that we all know the angle of the primary bright fringe

As a result, the gap between the two brilliant fringes with is

Step: 3 Calculating number of fringes: (part b)

Equation as

The maximum no of bright fringes of central increases as

So,the number of fringes on screen is

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