91影视

Given:

Angle of third order bright spot is ${胃}_3=65.0^{鈭�}$

Wavelength of red light is ${位}_1=700鈥�nm=700脳{10}^{-9}鈥�m$

Wavelength for violet light is ${位}_2=400鈥�nm=400脳{10}^{-9}鈥�m$

A diffraction grating is an optical component that has the ability to break light into its constituent wavelengths.

The angular position of the fringe is given by the following relation.

$\mathit{s}\mathit{i}\mathit{n}{\mathit{胃}}_{\mathbf{m}}\mathbf{=}\frac{\mathbf{m}\mathbf{位}}{\mathbf{d}}$

Here,$\mathit{位}$ is the wavelength of light used anddis the slit width.

The slit size is given as$d=\frac{m位}{\sin {胃}_m}$is a constant since the grating is not changing.

Therefore,

$\frac{n{位}_r}{\sin {胃}_{rn}}=\frac{m{位}_v}{\sin {胃}_{vm}}$

Here, subscript states that the value is of violet light and subscript states that the value is of violet light.

Now, take, n = 3 and m = 2

$$\begin{gathered} \sin {胃}_{v2}=\sin {胃}_{r3}\frac{2{位}_v}{3{位}_r} \\ =\sin 65掳脳\left(\frac{2脳400nm}{3脳700nm}\right) \\ =0.345 \\ {胃}_{v2}={\sin }^{-1}\left(0.345\right) \\ =20.2掳 \end{gathered}$$

Thus, the second-order bright spot for violet light is at angle $20.2掳$.