You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Moving Plane Mirror, Stationary Object

Suppose a lum...

Question

Suppose a luminous sphere of radius $R_{1}$ (such as the Sun) is surrounded by a uniform atmosphere of radius $R_{2} > R_{1}$ and index of refraction $n .$ When the sphere is viewed from a location far away in vacuum, what is its apparent radius when $R_{2} > n R_{1}$

Open in App

Solution

Assume the viewer is far away to the right. In ANS. FIG. P35.86(a), a ray directed toward the viewer comes tangentially from the edge of the glowing sphere and emerges from the atmosphere at angle $θ_{2} .$ The apparent radius of the glowing sphere is $R_{3}$ as shown. For the figure, we see that
$sin θ_{1} = \frac{R_{1}}{R_{2}} and sin θ_{2} = \frac{R_{3}}{R_{2}}$
Then, $n sin θ_{1} = 1.00 sin θ_{2}$
and $n \frac{R_{1}}{R_{2}} = \frac{R_{3}}{R_{2}} \to R_{3} = n R_{1}$

Suggest Corrections

Similar questions

Q. A hollow, neutral conducting sphere of inner radius

R_{1}

and outer radius

R_{2}

encloses a charge q inside it which is located at a distance d

(< R_{1})

from the centre of the spheres. The potential at the centre of the shell is

A metallic sphere of radius $R_{1}$ is charged to a potential V. If it is enclosed by a spherical conducting shell of radius $R_{2}$ and connected to it, its new potential will be

When two soap bubbles of radius $r_{1}$ and $r_{2}$ ( $r_{2}$ > $r_{1}$ ) coalesce, the radius of curvature of common surface is

Q. A solid sphere of radius

R_{1}

and volume charge density

ρ = \frac{ρ_{0}}{r}

is enclosed by a hollow sphere of radius

R_{2}

with negative surface charge density

σ

, such that the total charge in the system is zero.

ρ_{0}

is a positive constant and r is the distance from the centre of the sphere. The ratio

\frac{R_{2}}{R_{1}}

Q. The magnitudes of the gravitational force at distances

r_{1}

and

r_{2}

from the centre of a uniform sphere of radius

R

and mass

M

are

F_{1}

and

F_{2}

respectively. Then

Join BYJU'S Learning Program

Suppose a luminous sphere of radius R1 (such as the Sun) is surrounded by a uniform atmosphere of radius R2>R1 and index of refraction n. When the sphere is viewed from a location far away in vacuum, what is its apparent radius when R2>nR1

Suppose a luminous sphere of radius $R_{1}$ (such as the Sun) is surrounded by a uniform atmosphere of radius $R_{2} > R_{1}$ and index of refraction $n .$ When the sphere is viewed from a location far away in vacuum, what is its apparent radius when $R_{2} > n R_{1}$