X Reflection and Refraction

Example: 1 Calculate the minimum distance between object and its real image formed by convex lens of focal length F

(a) f (b) 2f (c) 3f (d) 4f         

Answer: Let the distance between object and real image formed by convex lens is d  and Let object image distance is x  ; then image distance is  d –x

By using Lense formula,
But, 1/v - 1/u = 1/f
So, 1/(d-x) - 1/(-x) = 1/f.
{x-(d-x)}/{x(d-x)} =1/f

{x-d+x}f =xd – x²

df = dx – x²

x² – dx + df = 0

Using quadratic equation,

For real value, D ³ 0

b² + 4ac  ³ 0

(-d)² – 4x1xdf ³ 0

d² – 4df ³ 0

d² ³ 0+4df

d ³  4f

Therefore, Let the distance between object and real image formed by convex lens is 4f.

Example: 2 A plane mirror makes an angle of 30o with horizontal. If a vertical ray strikes the mirror, find the angle between mirror and reflected ray [RPET 1997]

(a) 30^o (b) 45 ^o (c) 60 ^o (d) 90 ^o                                                  

Solution : (c)

Example: 3 A person is in a room whose ceiling and two adjacent walls are mirrors. How many images are formed [AFMC 2002]

(a) 5 (b) 6 (c) 7 (d) 8

Solution : (c)

The walls will act as two mirrors inclined to each other at 90^o and so sill form 360/90 -1= 3 images of the person.

Now these images with object (Person) will act as objects for the ceiling mirror and so ceiling will form 4 images as shown. Therefore total number of images formed = 3 + 4 = 7 

Note : The person will see only six images of himself I₁,I₂,I₃, I’₁,I’₂,I’₃

Example: 4 A ray of light makes an angle of 10 ^o with the horizontal above it and strikes a plane mirror which is inclined at an angle q to the horizontal. The angle q for which the reflected ray becomes vertical is

(a) 40 ^o (b) 50 ^o (c) 80 ^o (d) 100 ^o

Solution : (a) From figure  q+q+10 =  90 Þ q = 40^o

Example: 5:  Two vertical plane mirrors are inclined at an angle of 60o with each other. A ray of light travelling horizontally is reflected first from one mirror and then from the other. The resultant deviation is

(a) 60 ^o (b) 120 ^o (c) 180 ^o (d) 240 ^o

Solution : (d) By using formula deviation  (360 -2q ) =( 360 – 60x 2) = 240^o