Question

Two concave refracting surfaces of equal radii of curvature face each other in the air as shown in the figure. The point object O is placed midway between the centre and one of the poles. Then the separation between the images of O formed by each refracting surface is ______.

  

विकल्प

• 11.4 R

• 1.14 R

• 0.114 R

• 0.0114 R

Answer 1

Two concave refracting surfaces of equal radii of curvature face each other in the air as shown in the figure. The point object O is placed midway between the centre and one of the poles. Then the separation between the images of O formed by each refracting surface is 0.114 R.

Explanation:

 

I₁ due to refraction at the surface (1),

`1.5/V - 1/(R/2) = (1.5 - 1)/R`

⇒ `1.5/V = 2/R + 0.5/R`

⇒ `1.5/V = 2.5/R`

⇒ V = `3/5 R = 0.6 R`

I₂ due to refraction at the surface (2),

`1.5/V - 1/((-3R)/2) = (1.5 - 1)/(-R)`

⇒ `1.5/V = -2/(3R) - 0.5/R`

⇒ `1.5/V = (-3.5)/(3R)`

⇒ V = `(-4.5)/(3.5)R`

= `-9/7R`

= -1.285 R

Distance between I₁ & I₂ = 0.114 R