First slide

Diffraction

Question

Angular width of central maxima in the Fraunhofer diffraction pattern of a slit is measured. The slit is illuminated by light of wavelength $6000 Å$ . When the slit is illuminated by light of another wavelength, the angular width decreases by 30%. The wavelength of this light will be

Moderate

A

$6000 Å$
B

$4200 Å$
C

$3000 Å$
D

$1800 Å$

Solution

Angular width $β = \frac{2 λ}{d}$
$\Rightarrow \frac{β_{1}}{β_{2}} = \frac{λ_{1}}{λ_{2}} \Rightarrow \frac{β}{\frac{70}{100} β} = \frac{6000}{λ_{2}} \Rightarrow λ_{2} = 4200 Å$

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