Question

Light from a small object in air falls on a spherical glass surface (n = 1.5) of radius of curvature R. A real image of the object will be formed if the object distance u is related to R as ______.

विकल्प

• `u lt R/2`

• `R/2 lt u lt R`

• R < u < 2R

• u > 2R

Answer 1

Light from a small object in air falls on a spherical glass surface (n = 1.5) of radius of curvature R. A real image of the object will be formed if the object distance u is related to R as u > 2R.

Explanation:

Given: Refractive index of air (n₁) = 1

Refractive index of glass (n₂) = 1.5

Object distance = u, for a real object, u is negative (−u)

Radius of curvature = R

To find the condition for a real image, we use the formula for refraction at a single spherical surface:

`n_2/v - n_1/u = (n_2 - n_1)/R`

`1.5/v - 1/-u = (1.5 - 1)/R`

`1.5/v + 1/u = 0.5/R`

`1.5/v = 1/(2 R) - 1/u`

For a real image to be formed in the second medium (glass), the image distance (v) must be positive (v > 0):

`1.5/v gt 0`

⇒ `1/(2 R) - 1/u gt 0`

`1/(2 R) gt 1/u`

u > 2R