Question

the radius of currature of each surface of a biconvex lens is 20cm.
1) calculate its focal length if u of glass =1.5
2)calculate its focal length when it is immersed in water (u=1.33)
answer in above 100 words

Answer 1

use formula ,
1/f = (u -1){ 1/R1 - 1/R2 }
where f is the focal length
u is the refractive index of lens with respect to medium .
R1 and R2 is radius of curvature of lens .

here,
1) R1 = 20 cm
R2 = -20 cm
u = refractive index of lens/refractive index of medium = 1.5/1
u = 1.5

now,
1/f = (1.5 -1) { 1/20 - 1/(-20) }
= ( 0.5){ 2/20 }
= 1/20
f = 20 cm .
hence, focal length of biconvex lens = 20cm

2) here
R1 = 20 cm
R2 = -20 cm
u = refractive index of lens/refractive index of medium = 1.5/1.33 = 1.127

1/f = ( u -1) { 1/R1 - 1/R2}
=( 1.127 -1){ 1/20 - 1/(-20) }
=( 0.127){2/20}
=0.254×2/20
= 1/40

f = 40 cm
hence, focal length of lens when it imerged in liquid = 40 cm