Name: Reflecting Telescope
Uploaded: 2019-07-19
Duration: 6 min 40 s
Description: This telescope uses a single or a combination of curved mirrors that reflect light and form an image. Watch this amazing video to learn more.

Question

What is angle of minimum deviation? For refraction of light through a prism, establish the relation

μ = \frac{\sin (\frac{A + δ_{m}}{2})}{\sin (\frac{A}{2})}

; Where terms have usual meanings.

Accepted Answer

Angle of minimum deviation $(δ_{m i n})$ : The smallest angle at which light is bent by an optical instrument or a system like a lens. The angle of deviation is minimum if the incident and refracted rays are forming equal angles with the faces of prism.

Here in the given prism, $O P$ is the incidence ray, which is making the angle $i_{1}$ with normal, and $Q R$ is the angle of emergence, which is represented by $I_{2}$ . $A$ is the prism angle and $μ$ is the refractive index of the prism.

In case of minimum deviation:

$r_{1} = r_{2} = r$ and $i_{1} = i_{2} = i$ and $δ = δ_{m i n}$

Now, $A = r_{1} + r_{2} = 2 r \Rightarrow r = \frac{A}{2}$ ................................... $(1)$

Now, $A + δ = i_{1} + i_{2} = 2 i \Rightarrow i = \frac{A + δ_{m i n}}{2}$ ................................... $(2)$

Now using snell's law, $μ = \frac{\sin i}{s i n r}$ ................................... $(3)$

By substituting equation $(1)$ and $(2)$ in equation $(3)$ we get, $μ = \frac{\sin (\frac{A + δ_{m i n}}{2})}{\sin (\frac{A}{2})}$ .

Hence, the relation between refractive index and angle of deviation is established.

What is angle of minimum deviation? For refraction of light through a prism, establish the relation $μ = \frac{\sin (\frac{A + δ_{m}}{2})}{\sin (\frac{A}{2})}$ ; Where terms have usual meanings.

Important Questions on Ray Optics and Optical Instruments

Learn and Prepare for any exam you want !

What is angle of minimum deviation? For refraction of light through a prism, establish the relation μ=sinA+δm2sinA2; Where terms have usual meanings.

Important Questions on Ray Optics and Optical Instruments

Learn and Prepare for any exam you want !

What is angle of minimum deviation? For refraction of light through a prism, establish the relation $μ = \frac{\sin (\frac{A + δ_{m}}{2})}{\sin (\frac{A}{2})}$ ; Where terms have usual meanings.