Answer to Question #146739 in Optics for Promise Omiponle

Question

Suppose a 1.5 μm wide slit produces its first minimum for 410 nm violet light.

Randomized Variables
λv = 410 nm
λr = 730 nm
w = 1.5 μm


(a) Calculate the angle at which this occurs for violet light in degrees.
(b) Where is the first minimum (in degrees) for 730 nm red light?

Answer 1

(a) The angle at which this occurs for violet light θ = angular separation

For the 1^st minimum n = 1

$sinθ = \frac{λ_v}{w}$

$θ = sin^{-1}(\frac{λ_v}{w})$

$θ = sin^{-1}(\frac{410 \times 10^{-9}}{1.5 \times 10^{-6}}) \\ = sin^{-1}(0.2733) \\ = 15.86 \; degrees$

(b) For the red light:

$dsinθ = nλ_r \\ n = 1 \\ sinθ = \frac{λ_r}{w} \\ θ = sin^{-1}(\frac{λ_r}{w}) \\ θ = sin^{-1}(\frac{730 \times 10^{-9}}{1.5 \times 10^{-6}}) \\ = sin^{-1}(0.4866) \\ = 29.11 \; degrees$