A commercial diffraction grating has 500 lines per mm. When a student shines a 530...

Joseph Krupa

Joseph Krupa

Answered

2022-01-17

A commercial diffraction grating has 500 lines per mm. When a student shines a 530 nm laser through this grating, On the screen behind the grating, how many bright spots are visible?

Answer & Explanation

Papilys3q

Papilys3q

Expert

2022-01-18Added 34 answers

Step 1 
The condition for the diffraction grating is, 
dsinθ=mλ 
The angle is 90 degrees for bright fringes with the highest order. Any angle greater than 90 degrees will result in the diffraction going behind itself, which is not possible.
(1500×103)sin90=m(530×109m) 
(1500×103)sin90 
=3.77 
Choose the integer value of m 
So, the number of bright spots is, 
n=2m+1=2×3+1=7 
Hence, the number of bright spots is 7.

Piosellisf

Piosellisf

Expert

2022-01-19Added 40 answers

Step 1
The diffraction grating condition is,
dsinθ=mλ
m=dsinθλ
=(1500lesmm)sin90530×109m
=(103m500)sin90530×109m
=3.77
=3
Since for the maximum diffraction the angle is 90 degrees
So, the number of bright spots is,
n=2m+1=2(3)+1=7
alenahelenash

alenahelenash

Expert

2022-01-23Added 366 answers

Step 1 As per the given data, N=500 and λ=530nm Therefore, d=1N =1mm500 =2×106m d=2×106m Step 2 In diffraction method, 1) dsinθ=mλ Where, d is the width of the slit; m is the number of bright fringes on one side of central maxima; λ is the wavelength of the light used; And θ is the angle made by the light with bright fringe To find maximum bright fringes, θ=90 Step 3 Substitute all the given values in equation (1), (2×106)(sin90)=m(530×109) m=(2×106)(530×109) =2530×103 =3.7 m=3 Since it is always a whole number This means, the number of bright fringes above the central maxima are 3 and also below the central maxima are 3 Therefore, M=2m+1 =7

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