Answer to Question #110024 in Optics for Vidurjah Perananthan

Question

A grid is illuminated with the yellow light from a sodium lamp (λ = 589.3 nm).
You can then see 7 light rays behind the grille. The angle between the two outermost rays was measured at 105.4o. The same grid is then illuminated with light of wavelength 435 nm.
How many rays can you ser?




A beam of light from a laser hits a grid with the grid constant of 1.67 microns. Behind the grid, 5 rays can be observed. The angle between the outermost rays was measured to 94.1 degrees. Calculate the wavelength of the laser light.

Answer 1

a)

As per the given question,

wavelength of the yellow light $(\lambda)=589.3nm= 589.3\times 10^{-9}m$

$\lambda_1=435nm$

Angle$=105.4^\circ$

$d\sin\theta = n\lambda$

$\Rightarrow d=\dfrac{n\lambda}{\sin\theta}=\dfrac{7\times 589.3\times 10^{-9}}{\sin{105.4^\circ}}$ m

$m=\dfrac{d\sin\theta}{\lambda_1}=\dfrac{7\times 589.3\times 10^{-9}\sin{105.4^\circ}}{\sin{105.4^\circ}\times435\times 10^{-9}}$

$=\dfrac{7\times 589.3}{435}=9$

b) n=5

angle $(\theta)=94.1^\circ$

$d=1.67 microns=1.67\times 10^{-6}m$

$d\sin\theta= n\lambda$

$\lambda = \dfrac{d\sin \theta}{n}=\dfrac{1.67\times 10^{-6}\sin(94.1)}{5}$

$\lambda = 0.33\times 10^{-6}m$