​A small point object is placed in air at a distance of 60 cm from the convex spherical refracting surface of refractive index 1.5. If the radius of curvature of the spherical surface is 25cm, find the position of the image and power of the refracting surface.

Dear Student,
Please find below the solution to the asked query:

Since refraction at a spherical surface is given by:

n₂/v - n₁/u = (n₂-n₁)/R
where:
n₂ = refractive index of the refracting medium = 1.5
n₁ = refractive index of the medium in which the light was travelling initailly ( usually air) = 1
v = distance of image formed 
u = distance of the object from the refracting surface = -60 cm
R = Radius of curvature of the refracting surface = 25 cm

Now, 
substituting the values in the above equation we have:
1.5/v - 1/(-60) = (1.5-1)/25
1.5/v + 1/60 = 1/50
1.5/v = 1/50 - 1/60 
v / 1.5 = 300
v = 450 cm behind the spherical surface.


Now, 
Power of a spherical refracting surface = (n₂-n₁)/R ( in m) 
P = 0.5 / 0.25
P = 2 dioptre

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Satyendra Singh