Lens Cpp Iit Jee

CPP-11

Batches - PHONON

Class - XI

LENS
1.

A thin concavo-convex lens has two surfaces of radii of curvature R and 2R. The material of the lens has a refractive
index µ. When kept in air, the focal length of the lens :
(A) Will depend on the direction from which light is incident on it
(B*) Will be the same, irrespective of the direction from which light is incident on it
R
(C) Will be equal to µ  1

Sol.

From left to right 

(D*) Will be equal to

R
µ 1

1
1 
 1
 1 1
–
–
f L1 = (µ – 1)  – R –2 R  = (µ = 1)  2R R 





µ

1
 µ – 1
f L1 = – 2 R

From right to left 

1
f L2 = (µ – 1)

=–



 1
1 
–

 = (µ – 1)
2 R (  R ) 


convex
surface
2R

concave
surface
R

 1 1
– 

 2R R 

 µ – 1
2R

1
1
2R
= f = – ( µ –1)
f L1
L2

Option (B) and (D) are correct.
2.

Sol.

An object is placed 10 cm away from a glass piece (n = 1.5) of length
20 cm bound by spherical surfaces of radii of curvature 10 cm. Find the
position of the final image formed after twice refractions.
Ans. [50 cm]
Refraction at first surface :

20 cm

air

air
B

object

A
10 cm ROC = 10cm

n = 1.5
ROC = 10cm

1.5
1
1.5 –1
– (–10) = (10)  V1 = – 30 cm from A
V1

Refraction at second surface.
1
1.5
1 – 1.5
– (–50) = (–10)  V2 = +50 cm from B
V2

Hence final image will be 50 cm from B.
3.

A concave mirror of radius R is kept on a horizontal table (figure). Water (refractive
index = ) is poured into it upto a height h. What should be distance of a point
object from surface along principal axis so that its final image is formed on itself.
Consider two cases.
(i) h 0
(ii) in terms of h

Page 1

( R  h)
R
; (ii)
]



Ans. [(i)
Sol.

Object should appear to be at distance R from mirror.

µ(d) + h = R

if

Sol.

d=

h

h << R



4.

d

 R–h

d= 
 µ 



c

R
µ

A person's eye is at a height of 1.5 m. He stands infront of a 0.3 m long plane mirror which is 0.8 m above the ground,
The length of the image he sees of himself is :
(A) 1.5 m
(B) 1.0 m
(C) 0.8 m...