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

A ray of light is incident on a glass sphere at an angle

α

. Angle of refraction, at the surface on which it is incident, is

β

. What is the angle by which the ray is deviated as it comes out of the sphere?

Accepted Answer

Given that a ray of light is incident on a glass sphere at an angle $α$ .

Given that angle of refraction at the surface on which it is incident is $β$ .

Let us consider that the point of incidence and point of emergence be $A$ and $B$ and let $O$ be the centre of the sphere.

As we know that any normal to any point on the surface passes through the centre $O$ , a triangle $O A B$ will be formed.

Since $O A = O B = R a d i u s$ .

$\Rightarrow ∠ O A B = ∠ O B A = β$

Let us consider the angle of emergence is $e$ and glass has a refractive index $μ$ .

We know that snell's law is $μ_{1} \sin (i) = μ_{2} \sin (r)$ .

Applying snell's law at the surface of incidence,

$1 \times \sin (α) = μ \times \sin (β) . . . (1)$

Similarly for the emerging surface, we get,

$μ \times \sin (β) = 1 \times \sin (e) . . . (2)$

By comparing the equations $(1)$ and $(2)$ we can say that $e = α$

So the angle by which the ray is deviated as it comes out of the sphere will be $α$ .

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