A monochromatic light wave is incident normally on a glass slab of thickness as shown in the figure. The refractive index of the slab increases linearly from n1 to n2 over the height of h. Which of the following statements is/are true about the light wave emerging out of the slab?
Monochromatic light wave
Monochromatic light wave
- It will not deflect.
- It will deflect by an angle \(tan^{-1}[\frac{(n_2-n_1)d}{h}]\)
- The deflection angle depends only on (n2 - n1) and not on the indivisual values of n1 and n2
- It will deflect up by an angle \(tan^{-1}[\frac{(n_2^2-n_1^2)d}{2h}]\)
The Correct Option is B, D
Approach Solution - 1
\(t=\frac{d}{\frac{c}{n_1}}=\frac{n_1d}{c}\)
in time t wavefront at B travel S1; \(S_1=\frac{c}{n_2}\times\frac{n_1d}{c}\Rightarrow\frac{dn_1}{n_2}\)
When the wave front of B reaches at the end of the slab then t1 =\((\frac{d-s_1}{c})n_2\Rightarrow \frac{d[n_2-n_1]}{c}\)
in t1 time, wavefront at A travel \(\Rightarrow\) S2
S2=ct1=d[n2-n1]
\(tan\theta=\frac{(n_2-n_1)d}{n}\Rightarrow \theta=tan^{-1}\frac{(n_2-n_1)d}{h}\)
Approach Solution -2
Dashed lines MN and PQ represent incident wave fronts.
Just before entering the slab, PQ is at a maximum.
Points P1 and Q1 are on the other side of the slab.
Therefore, P1 will be ahead by n2d compared to P, and Q1 will be ahead by n1d compared to Q.
The right side of the medium is homogeneous.
To have the same path lead as P1, Q' must travel to Q1, so 𝑛2𝑑=𝑛1𝑑+ℎsin𝜃.
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Concepts Used:
Ray Optics and Optical Instruments
Optics, deals with the determination of behaviour and the properties of light, along with its interactions with the matter and also with the instruments that are used to detect it.
Ray optics is also known as the geometrical optics and it is a branch of science which describes light propagation.
Reflection is the change in direction of light at an interface in-between two different media so that the wave-front returns into a medium from which it was originated.
Speed of light is the rate at which the light travels in free space.
A phenomenal change in image formed when the light is passed from one medium to another which is called Refraction.
Total Internal Reflection is the reflection of light when the light ray enters into a rarer medium from a denser medium and the angle of incidence is higher than the critical angle of incidence then that light ray will be reflected back to the denser medium.
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