Question

A thick plane-convex lens made of crown glass (refractive index 1.5) has thickness of 3 cm at its centre. The radius of curvature of the spherical surface is 5 cm.
An link mark made at the centre of its plane face, when viewed normal through the curved face, appears to be at a distance x from the curved face. Then, x is equal to
A. 2cm
B. 2.1cm
C. 2.3cm
D. 2.5cm

Answer 1

Explanation:

A thick plano convex lens made of crown glass (refractive index 1.5) has a thickness of 3cm at its centre. The radius of curvature of its curved face is 5cm. An ink mark made at the centre of its plane face, when viewed normally through the curved face, appears to be at a distance ‘x’ from the curved face,and we have to determine the value of ' x'

According to the picture , the ray of light gets refracted at tge interface between the air and the lens  from the object 'p' and 'I' is the refracted image of 'p'

object distance 'u'= BO

Image distance 'v'/'x' = BI

we know

n2/v - n1/u = (n2- n1) / R

o,r 1/v - 1.5/(-3 )= (1-1.5)/ (-5) [where n2= 1, n1= 1.5 ,u= -3 ,R= -5]

so 1/v = -6/15

or, v = -2.5

so,x is equal to 2.5 cm