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
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]
Example: 3 A person is in a room whose ceiling and two adjacent walls are mirrors. How many images are formed [AFMC 2002]
Solution : (c)
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
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
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
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
Example: 6: Size of image of an object by a mirror having a focal length of 20 cm is observed to be reduced to 1/3rd of its size. At what distance the object has been placed from the mirror? What is the nature of the image and the mirror?
Given: f=20 cm, h0:h1=1/3. m=h1/h0=3/1 m=3. Also m= -v/u 3=-v/u u= -3v
Now, 1/f= 1/u+1/v. 1/20= 1/-3v+1/u
1/20=2/3v v=40/3 cm
Now, U=-3v u= -3x (40/3) u=-40 cm. Ans.
What is Lateral Shift?
When a ray of light is incident obliquely on a parallel sided glass slab the emergent ray shifts laterally. The perpendicular distance between the direction of the incident ray and emergent ray is called “lateral shift’’.
The factors on which the lateral displacement depends are:
Thickness of the refracting material and the refractive index of the material.
What is optical density?
Optical density is the measure of absorption per unit distance of incident light by a material. When a beam of light enters into any material, some of it is absorbed by the material. This absorption rate varies from material to material and is also different for radiation of various wavelengths for a particular material.
What is a critical angle?
The angle of incidence in the denser medium for which the angle of refraction in rarer medium is 900
When
light passes from one medium to other, it bends from its path which is called
refraction. When a light ray passes from denser to rarer medium,
at some angle of incidence it does not go out of the denser medium but just
grazes along the boundary (i.e. angle of refraction = 900). This angle of
incidence is called critical angle.
Now, if you increase this angle of incidence, light ray is reflected back into the denser medium, which is called total internal reflection. The light ray is reflected every time it hits the boundary because angle if incidence is equal to angle of reflection, and is not able to come out of the medium. This phenomenon is called total internal reflection.
The conditions for total internal reflection are:
(i) the light ray must be travelling from optically denser medium to rarer medium and
(ii) the angle of incidence must be greater than the critical angle.
Optical fiber communication uses the principle of total internal reflection for transferring data through optical fibers.
What
is meant by ‘total internal reflection’? State two essential conditions for
total internal reflection to take place. With the help of a ray diagram,
illustrate an application of total internal reflection.
When
light passes from one medium to other, it bends from its path which is called
refraction. When a light ray passes from denser to rarer medium,
at some angle of incidence it does not go out of the denser medium but just
grazes along the boundary (i.e. angle of refraction = 900). This angle of
incidence is called critical angle.
Now, if you increase this angle of incidence, light ray is reflected back into the denser medium, which is called total internal reflection. The light ray is reflected every time it hits the boundary because angle if incidence is equal to angle of reflection, and is not able to come out of the medium. This phenomenon is called total internal reflection.
The conditions for total internal reflection are:
(i) the light ray must be travelling from optically denser medium to rarer medium and
(ii) the angle of incidence must be greater than the critical angle.
Optical fiber communication uses the principle of total internal reflection for transferring data through optical fibers.
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