Question 105: Ray Optics

Question

A spherical surface separates two media of refractive indices 1 and 1.5 as shown in figure. Distance of the image of an object ' O ', is :
( C is the center of curvature of the spherical surface and R is the radius of curvature)

Accepted Answer

To determine the image distance when a spherical surface separates two media with refractive indices of 1 and 1.5:
Use the lens maker's formula for a spherical surface:
$    \frac{\mu_2}{v} - \frac{\mu_1}{u} = \frac{\mu_2 - \mu_1}{R}    $
Where:
$\mu_1$ = 1 (refractive index of the first medium)
$\mu_2$ = 1.5 (refractive index of the second medium)
$u$ = -0.2 m (object distance, negative as per convention)
$R$ = 0.4 m (radius of curvature)
Substituting the known values:
$    \frac{1.5}{v} - \frac{1}{-0.2} = \frac{1.5 - 1}{0.4}    $
Simplify the equation:
$    \frac{1.5}{v} = \frac{0.5}{0.4} - \frac{1}{0.2}    $
Calculate:
$    \frac{1.5}{v} = -\frac{1.5}{0.4}    $
Solve for $v$:
$    v = -0.4 \, 	ext{m}    $
The negative sign indicates that the image is 0.4 meters to the left of the spherical surface.

Answer

0.24 m left to the spherical surface

Answer

0.24 m right to the spherical surface

Answer

0.4 m left to the spherical surface

Answer

0.4 m right to the spherical surface

Ray Optics

A spherical surface separates two media of refractive indices 1 and 1.5 as shown in figure. Distance of the image of an object ' O ', is : ( C is the center of curvature of the spherical surface and R is the radius of curvature)

Choose the correct answer: