A plano-convex lens has thickness 4cm. When places on a horizontal table with the curved surface in contact with it, the apparent depth of the bottom-most point of the lens if found to be 3cm. If the lens is inverted such that the plane face is in contact with the table, the apparent depth of the center of the plane face of the lens is face of the lens is found to be `25//8` cm. Find the focal length of the lens.

Options

A. 85cm
B. 59cm
C. 75cm
D. 7.5cm

Answer

C

Explanation

In first case refraction of the rays, takes place from a plane surface, so we can use `d_("app")= (d_("actual"))/(mu)`
`3=(4)/(mu) rArr mu= (4)/(3)`
where, `d_("app") and d_("actual")=` apparent and real depth, respectively. Now, in second case, as from Fig (b), refraction takes place from a spherical surface, so
`(mu_(2))/(v)-(mu_(1))/(u)= (mu^(2)-mu_(1))/(R )`
or `(1)/((-25//8))-(4//3)/((-4))=(1-4//3)/(-R)`
or `(1)/(3R)= (1)/(3)- (8)/(25)= (1)/(75)` R=25cm
Now, using Lens. Makers formula, to calculate focal length `(1)/(f)= (mu-1) ((1)/(R_(1))- (1)/(R_(2)))`
`(1)/(f)= ((4)/(3)-1) ((1)/(oo)- (1)/((-25)))= (1)/(75)`
f= 75cm