Physics Class 12 NCERT Solutions: Chapter 9 Ray Optics and Optical Instruments Part 8 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Total Internal Reflection

Q: 16. A small pin fixed on a table top is viewed from above from a distance of . By what distance would the pin appear to be raised if it is viewed from the same point through a thick glass slab held parallel to the table? Refractive index of glass . Does the answer depend on the location of the slab?


Actual depth of the pin,

Apparent of the

Refractive index of glass,

Ratio of actual depth to the apparent depth is equal to the refractive index of glass, i.e..

The distance at which the pin appears to be raised

For a small angle of incidence, this distance does not depend upon the location of the slab.

Q: 17. (A) Figure shows a cross-section of a ‘light pipe’ made of a glass fibre of refractive index 1.68. The outer covering of the pipe is made of a material of refractive index 1.44. What is the range of the angles of the incident rays with the axis of the pipe for which total reflections inside the pipe take place, as shown in the figure.

(B) What is the answer if there is no outer covering of the pipe?

Q_17_the No Outer Covering of the Pipe


(A) Refractive index of the glass fibre,

Refractive index of the outer covering of the pipe,

Angle of incidence

Angle of refraction

Angle of incidence at the interface

The refractive index of the inner core – outer core interface is given as:

For the critical angle, total internal reflection (TIR) takes place only when, i.e.. ,

Maximum angle of reflection,

Let, be the maximum angle of incidence.

The refractive index at the air – glass interface,

We have the relation for the maximum angles of incidence and reflection as:

Thus, all the rays՚ incident at angles lying in the range will suffer total internal reflection.

(B) If the outer covering of the pipe is not present, then:

Refractive index of the outer pipe, Refractive index of air

For the angle of incidence , we can write Snell՚s law at the air – pipe interface as:

Since , all incident rays will suffer total internal reflection.

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