HC Verma Class 10 Light Reflection and Refraction Solutions

 

HC Verma Class 10 Light Reflection and Refraction Solutions

A . Very-Short-Answer Questions

1)      From which surface of a mirror-the polished surface or the silvered surface-does most of the light?

      Silvered surface is used in a mirror because silver is one of the metal which reflects the most light which is incident on it. Hence polished silver is used in a mirror because of its ability to reflect the maximum light incident on it without absorbing it.

2)      In which kinds of mirrors-plane, concave or convex-can you get a virtual image of an object placed in front of it?

      Convex and plane mirror always give you virtual image. however concave give you virtual, when object is between focus and pole

3)      What is the principal axis of a spherical mirror?

      The principal axis is called a line that passes via the centre of the surface of a spherical mirror or lens and through the centre of curvature of all segments of the mirror or lens.

4)      A concave mirror forms a real image of the same size as that of object. Where is the object placed?

      The object should be placed at centre of curvature

5)      Can a convex mirror form a real image an object?

      Convex mirrors can produce real images as well. If the object is virtual, i.e., if the light rays converging at a point behind a plane mirror (or a convex mirror) are reflected to a point on a screen placed in front of the mirror, then a real image will be formed.

6)   A ray ACB is incident on a spherical mirror whose centre curvature is C. In which direction will it reflect?

     The ray will go back along the path ACB.

7)  What the sign of the object-distance u when an object placed before a concave mirror?

      The sign of objects distance when an object is placed before a concave mirror is - (Minus ).

8)      Where can the position of an object if a concave mirror forms its erect and virtual image?

      Concave mirror forms an erect, virtual and enlarged image when the object is between focus and pole of mirror.

9)      A mirror has focal length f = +10 cm. Is it convex.

         It is a convex mirror because focal length is always positive in convex mirror and negative in concave mirror.

1     What are the values of the angle of incidence and the angle of reflection for normal incidence on plane mirror?

      For normal incidence, the incident ray is along the normal itself. So the angle of incidence is 0. From the laws of reflection, the angle of incidence is equal to the angle of reflection. So, the angle of reflection is also 0.

B. Short-Answer Questions

1)      What is silvering of a mirror?

      Silvering is a chemical process of coating a non-conductive substrate like glass with a reflective substance, to produce a mirror.

2)      Write the two laws of reflection of light.

      Laws of reflection are: (i) The incident ray, the reflected ray and the normal ray at the point of incidence, lie in the same plane. (ii) The angle of incidence is equal to the angle of reflection.

3)   What do you understand by the radius of curvature of a spherical mirror?

      The radius of curvature of a spherical mirror is the radius of the circle of which the spherical mirror is a part.

4)   What is the difference between a real image and a virtual image?

          An image formed when the light rays converge at a particular point after refraction and reflection is known as a real image. An image formed when rays appear to meet a particular point after the reflection from the mirror is known as a virtual image.

6)      Convex mirrors are used as rear-view mirrors in scooters, motorcycles, etc. Explain  why.

         We prefer a convex mirror as a rear-view mirror in vehicles because it gives a wider field of view, which allows the driver to see most of the traffic behind him. Convex mirrors always form a virtual, erect, and diminished image of the objects placed in front.

1)      Describe a method to measure the focal length of a concave mirror.

        positive, whereas that of the concave mirror is negative. The same can also be proved by using the mirror formula: (1/f = 1/v +1/u).

2)      Write the sign convention used for spherical mirrors.

        Sign is taken as + (positive) behind the spherical mirror. For example if an image is formed behind the mirror, the distance of image is taken as + (positive) from pole along the principal axis. The height of is taken as + (positive) above the principal axis and taken as – (negative) below the principal axis.

3)

D. Numerical Problems

1)      An object is placed at a distance of 12 cm from a concave mirror of radius of curvature 16 cm. Find the position of the image.

The expression for the focal length is as follows;

Here, R is the radius of curvature.

Put R= 8 cm.

The expression for the mirror's formula is as follows;

Here, u is the object distance, v is the image distance and f is the focal length.

Calculate the position of the image.

Put f= - 8 cm and u= -12 cm.

Therefore, the position of the image is - 24cm.

3)      The image of an object placed 16 cm from concave mirror is formed at a distance of 24 cm mirror. Calculate the possible focal length of the concave mirror from this information.

4)      An object is placed 20 cm from a convex image is formed 12 cm from the mirror. Find the focal length of the mirror.

5)      Find the position, size and nature of the image formed by a spherical mirror from the following data.

              f = -12 cm,

                u =-36 cm,

                h_o = 2 cm

Nature of image: Real and inverted
position:
1/v+1/u=1/f
=>v=-18cm
size:
m= height of image/height of object=-v/u
=> height of image =-1
therefore diminished

E . Numerical Problems

1)      

2)      An object is placed 24 cm from a concave mirror. Its image is inverted and double the size of the object. Find the focal length of the mirror and the position where the image is formed.

          Given

m = -2 (concave mirror)
u = -24 cm

m = -v/u
-2 = -v/-24
v = - 48 cm

1/f = 1/v + 1/u
1/f = 1/-48 + 1/-24
1/f = -3/48
1/f = -1/16
f = -16 cm

3)     Where should an object be placed before a concave mirror of focal length 20 cm so that a real image is formed at a distance of 60 cm from it?

            for a real image, image distance must be of same sign as that of object's distance.

Considering the object to be on positive side, and by using mirrors formula

So, that means

4)      An object is placed at a distance of 12 cm from a convex mirror of radius of curvature 12 cm. Find the position of the image.

             

  

6)     When a concave mirror is placed facing the sun, the sun's rays converge to a point 10 cm from the mirror. Now, an erect, 2-cm-long pin is placed on the principal axis of the mirror. If you want to get the image of the pin on a card, where would you place the card? What would be the nature and height of the image?

      Concave mirror converges the rays of light to the point know as principal focus of the mirror.
Hence the focal length of the concave mirror is 10 cm

f = -10 cm
h₁ = +2 cm
u = -15 cm
h₂ & v = ?

Using mirror formula ;

1/f = 1/v + 1/u

(1/-10) = (1/v) + (1/-15)
1/v = (1/15) - (1/10)
1/v = (2-3)/30
v = -30
_________________________
Hence in order to get the image of a pin on a card, the card should be placed 30 cm in front of a concave mirror.
============================
m = (-v/u) = h₂/h₁

-(-30/-15) = h₂/2
h₂ = -4 cm
_________________________
The nature of image is Real, inverted and magnified i.e four times that of object.

F. Objective Questions

I. Pick the correct option.

1)       A mirror forms a virtual image of a real object.

(a) It must be a convex mirror.

(b) It must be a concave mirror.

(c) It must be a plane mirror.

(d) It may be any of the mirrors mentioned above.

D

It may be any of the mirrors mentioned above.

            2)      The angle of incidence is the angle between

(a) the incident ray and the surface of the mirror

(b) the reflected ray and the surface of the mirror

(c) the normal to the surface and the incident ray

(d) the normal to the surface and the reflected ray

Correct option------(d)

           3)     The angle of reflection is the angle between

(a) the incident ray and the surface of the mirror

(b) the reflected ray and the surface of the mirror

(c) the normal to the surface and the incident ray

(d) the normal to the surface and the reflected ray

(c) the normal to the surface and the incident ray

4) An object is placed at the centre of curvature of a concave mirror. The distance between its         image and the pole is

(a) equal to f

(b) between f and 2f

(c) equal to 2f

(d) greater than 2f

(c) equal to 2f

5) An object of size 2.0 cm is placed perpendicular to the principal axis of a concave mirror. The      distance of the object from the mirror equals the radius of curvature. The size the image will be

(a) 0.5 cm

(b) 1.0 cm

(c) 1.5 cm

(d) 2.0 cm

  (a) 0.5 cm

6) The magnification m of an image formed by a spherical mirror is negative. It means, the image is

(a) Samller than the object

(b) larger than the object

(c) erect

(d) inverted

The image is inverted

 

(7) A point object is placed on the principal axis spherical mirror. The object-distance u is

(a) definitely negative

(b) definitely positive

(c) positive if the object is to the left of the centre curvature

(d) positive if the object is to the right of the centre of curvature

(a) definitely negative