Answer to Question #146741 in Optics for Promise Omiponle

Question

Consider 575 nm wavelength yellow light falling on a diffraction grating having 1500 lines per centimeter.

Randomized Variables
λ = 575 nm


Find the angle (in degrees) for the third-order maximum for the yellow light.

Answer 1

The wavelength of yellow light λ = 575 nm = 5.75 \times 10^{-7} \; m

The number of lines N = 1500 lines per cm

$N= 1.5 \times 10^5$

The slit separation:

$d = \frac{1}{N}$

$d = 6.67 \times 10^{-6} \; m$

Let the angle for third-order maximum be theta

$d \times sinθ = n \times λ$

For third maximum

$6.67 \times 10^{-6} \times sinθ = 3 \times 5.75 \times 10^{-7}$

sinθ = 0.2586

θ = 14.98 degree

The angle for the third-order maximum for the yellow light is 14.98 degree.