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if 500-nm and 650-nm light illuminates twoslits that are separated by 0.50 mm, how farapart are the second-order maxima for thesetwo wavelengths on a screen 2.0 m away?



Answer :

For 500nm the second order maxima 2m away would be 1cm

For 650nm the second order maxima 2m away would be 1.12 cm

How to calculate second order maxima?

Maxima and minima are the maximum or the minimum value of a function within the given set of ranges.

The separation between the second order maxima is: ymax=2cm y max = 2 c m .

Calculation:

Assumption of infinite source distance gives plane wave at  slit. So, all amplitudes are in phase.

Here, sepration between 2nd order maxima will be given by

= 2(yd) = 2 (m+1/2) lamda×D/d

= 2 (2+1/2) lamda D/d = 5 lamda D/d

Here, d= 0.50mm=0.50×10^-3m

D=2m

For lambda = 500nm

Separation = 5 lamda D/d = 5(5×10^-7m)(2m)/(0.5×10^-3m) = 1 CM

For lamda = 650nm

Separation = 5 lamda D/d= 5(650×10^-9m) (2m) /(0.5×10^-3m) = 1.12cm

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