A parallel narrow beam of light is incident on the surface of a transparent hemisphere of radius R and refractive index μ =1.5 as shown. The distance of the image formed by refraction only (at the spherical surface only) from P is

Question

A parallel narrow beam of light is incident on the surface of a transparent hemisphere of radius R and refractive index μ =1.5 as shown. The distance of the image formed by refraction only (at the spherical surface only) from P is <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-fhmsenmoxjx1y6hd.jpg" /> (A) (R/2) (B) 3R (C) (R/3) (D) 2R

Tardigrade Admin · Accepted Answer

Applying, (μ 2/v)-(μ 1/u)=(μ 2 - μ 1/R) we get, (1 . 5/v)-(1/∞ )=(1 . 5 - 1 . 0/+ R) ∴ v=+3R .

Q. A parallel narrow beam of light is incident on the surface of a transparent hemisphere of radius $R$ and refractive index $μ = 1.5$ as shown. The distance of the image formed by refraction only (at the spherical surface only) from $P$ is

$\frac{R}{2}$

$3 R$

$\frac{R}{3}$

$2 R$

Applying, $\frac{μ _{2}}{v} - \frac{μ _{1}}{u} = \frac{μ _{2} - μ _{1}}{R}$ we get,
$\frac{1.5}{v} - \frac{1}{\infty} = \frac{1.5 - 1.0}{+ R}$
$∴ v = + 3 R$ .

Q. A parallel narrow beam of light is incident on the surface of a transparent hemisphere of radius R and refractive index μ=1.5 as shown. The distance of the image formed by refraction only (at the spherical surface only) from P is

2R​

3R

3R​

2R