A diffraction grating 19.2 mm wide has 6010 rulings. Light of wavelength 337 nm is incident perpendicularly on the grating. What are the (a) largest, (b) second largest, and (c) third largest values of θ at which maxima appear on a distant viewing screen?

(a). The largest value of θ is 71.9°.

(b). The second largest value of θ is 57.7°.

(c). The third largest value of θ is 47.7° .

Explanation:

Given that,

Width of diffraction grating

Number of rulings

Wavelength = 337 nm

We need to calculate the distance between adjacent rulings

Using formula of distance

Put the value into the formula

We need to calculate the value of m

Using formula of constructive interference

Here, m = 0,1,2,3,4......

=wavelength

For largest value of  θ

Put the value into the formula

(a). We need to calculate the largest value of θ

Using formula of constructive interference

Now, put the value of m in to the formula

(b). We need to calculate the second largest value of θ

Using formula of constructive interference

Now, put the value of m in to the formula

(c). We need to calculate the third largest value of θ

Using formula of constructive interference

Now, put the value of m in to the formula

Hence, (a). The largest value of θ is 71.9°.

(b). The second largest value of θ is 57.7°.

(c). The third largest value of θ is 47.7° .

the working equation for the angular size is the product of the physical size and 360 degrees divided by the product of two pi and distance from earth. the minimum size would be 0.559 degrees while the maximum size would be 0.49 degrees. 

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