Name: Optical Instruments: Spectrometer
Uploaded: 2019-07-19
Duration: 7 min 33 s
Description: The basic function of a spectrometer is to take in light, break it into its spectral components, digitise the signal as a function of wavelength, and read it...

Question

Derive expression for deviation produced by prism.

Accepted Answer

Angie of deviation produced by prism: Let light ray $P Q$ is incident on one of the refracting faces of the prism. The angles of incidence and refraction at the first face $A B$ are $i_{1}$ and $r_{1}$ . The path of the light inside the prism is $Q R .$ The angle of incidence and refraction at the second face $A C$ is $r_{2}$ and $i_{2}$ respectively. $R S$ is the ray emerging from $p$ the second face. Angle $i_{2}$ is also called angle of emergence. The angle between the direction of the incident ray $P Q$ and the emergent ray $R S$ is called the angle of deviation $d .$

The two normals drawn at the point of incidence $Q$ and emergence $R$ are $Q N$ and $R N$ . They meet at point $N .$ The incident ray and the emergent ray meet at a point $M .$

The deviation $d$ at the surface $AB$ is, $∠ RQM = d_{1} = i_{1} - r_{1}$ .

The deviation $d_{2}$ at the surface $AC$ is, $∠ QRM = d_{2} = i_{2} - r_{2}$ .

Total angle of deviation $d$ produced is, $d = d_{1} + d_{2}$ .

Substituting for $d_{1}$ and $d_{2}$ , $d = (i_{1} - r_{1}) + (i_{2} - r_{2}) . . . . . . (i)$ .

In the quadrilateral $AQNR$ , two of the angles (at the vertices $Q$ and $R$ ) are right angles. Therefore, the sum of the other angles of the quadrilateral is $180 °$ .

$∠ A + ∠ QNR = 180 °$ .

From the $△ QNR$ , $r_{1} + r_{2} ∠ QNR = 180 °$

Comparing these two equations we get $r_{1} + r_{2} = A$ . By substituting this value in equation $(i)$ we get, $d = i_{1} + i_{2} - A .$

Thus, the angle of deviation depends on the angle of incidence angle of emergence and the angle for the prism.

Derive expression for deviation produced by prism.

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