You are to determine the wavelengths of two different color laser beams by obser

Question

You are to determine the wavelengths of two different color laser beams by observing interference patterns using a double slit device with slit separation of 0.098 mm. You place a screen exactly 91 cm away from the double slit.

(a) With one laser beam, the third dark band appears on the screen 1.530 cm away from the central bright band. What must be the wavelength of this laser beam?
nm

(b) With the second laser beam, you find the second bright band appearing on the screen 0.8989 cm away from the central bright band. What must be the wavelength of this second laser beam?
nm

Explanation / Answer

a)
condition of minima,
y = (m-1/2)* *D/d
here m = 3
y = 1.530 cm = 1.530*10^-2 m
D = 91 cm = 0.91 m
d = 0.098 mm = 9.8*10^-5 m

y = (5/2)* *D/d
1.530*10^-2 = (5/2)* *(0.91)/(9.8*10^-5)
= 6.59*10^-7 m
    = 659 nm

Answer: 659 nm

b)
condition of maxima ,
y = m* *D/d
here m = 2
y = 0.8989 cm = 8.989*10^-3 m
D = 91 cm = 0.91 m
d = 0.098 mm = 9.8*10^-5 m

y = m* *D/d
8.989*10^-3 = 2 * * (0.91) / (9.8*10^-5)
=4.84*10^-7 m
    = 484 nm

Answer: 484 nm

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