Monday, November 5, 2012

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) 30o (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 90o 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 = 40o
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) = 240o

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