Question

(a) Under what conditions is the phenomenon of total reflection of light observed? Obtain the relation between the critical angle of incidence and the refractive index of the medium. 

(b) Three lenses of focal length +10cm, -10cm and +30 cm and arranged co-axially as in the figure given below. Find the position of the final image formed by the combination.

Answer 1

(a) Two essential conditions for total internal reflection are: 

• Light should travel from a denser medium to a rarer medium, 

• Angle of incidence in denser medium should be greater than the critical angle for the pair of media in contact.

Critical angle for a pair of media is contact is the angle of incidence in the denser medium corresponding to which angle of refraction in the rarer medium is 90°.

RELATION BETWEEN REFRACTIVE INDEX AND CRITICAL ANGLE :

When i = i_c, r = 90° 

Applying snell’s law, 

n₂ sini_c = n₁ sin90°, 

where r = 90° when i = i_c

n₂ = refractive index of denser medium 

n₁ = refractive index of rarer medium.

(b) For I^st lens : 

u₁ = -30 cm;

f₁ = +10cm; 

v₁ =?

Image formed by I^st lens serves as object for second lens at a distance = (15 – 5 )=10 cm, to the right of second lens, and the object is virtual.

For 2^nd lens:

The virtual image is formed at infinity to the right of 2^nd lens. This acts as an object for 3^rd lens. 

For 3^rd lens : 

u₃ = ∞; 

f₃ = 30 cm; 

v₃ = ?

∴ The final image is formed at 30 cm to the right of third lens.