Question

A parallel beam of light is allowed to fall on a transparent spherical globe of diameter 30cm and refractive index 1.5. The distance from the centre of the globe at which the beam of light can converge is ______ mm.

Options

• 227

• 226

• 222

• 225

Answer 1

A parallel beam of light is allowed to fall on a transparent spherical globe of diameter 30cm and refractive index 1.5. The distance from the centre of the globe at which the beam of light can converge is 225 mm.

Explanation:

Parallel Beam of light strikes at surface 1

Thus, 1^st refraction takes place at surface 1

and, 2^nd refraction takes place at surface 2

`mu_2/"v"-mu_1/"u" = (mu_2 -mu_1)/"R"`

Refraction at surface 1

All distances are measured from A

⇒ `1.5/"v" -1/(- oo) = (1.5-1)/(+15)`     ...[Given: u = –∞, v = ??, μ₂ = 1.5, μ₁ = 1, R = +15 cm]

`1.5/"v" = 0.5/15`

V = +45 cm

for refraction at surface 2

All distance will be measured from B

Image after refraction at surface 1 will play role of object for surface 2

`mu_2/"v"-mu_1/"u" = (mu_2 -mu_1)/"R"`

`1/"v" - 1.5/(+15) = (1-1.5)/(-15)`

`1/"v" - 1/10 = 0.5/(-15)`

`1/"v" = 1/30+1/10`

v = `300/40`

= 7.5 cm

Thus, distance of final image from B is 7.5 cm

Thus, beam of light converges at point

15 + 7.5 = 22.5 cm = 225 mm from centre of sphere.