Question Bank: Reflection of light at curved surfaces

1. Reflection of light at curved surfaces

I. REFLECTIONS ON CONCEPTS :

1. Where will the image be formed when we place an object on the principal axis of a concave mirror at a point between focus and centre of curvature ?

Ans: When we place an object on the principal axis of a concave mirror at a point between focus (F) and centre of curvature (C), the image is formed beyond the centre of curvature.

2. State the differences between convex and concave mirrors.

Ans:

Convex Mirror	Concave Mirror
1) A parallel beam of light falling on this mirror appears to diverge from a point after reflection.	1) A parallel beam of light falling on this mirror converges at a point after reflection.
2) The reflecting surface of convex mirror is bulged out.	2) The reflecting surface of a concave mirror curves inward.
3) Radius of curvature and focal length are taken as positive in sign conversion.	3) Radius of curvature and focal length are taken as negative in sign conversion.
4) It's magnification is positive only.	4) It's magnification may be both positive and negative.
5) Magnification of convex mirror is in between zero and one.	5) Magnification value of concave mirror having all values.
6) The image formed by convex mirror always diminished.	6) The image formed by concave mirror may be magnified or diminished.
7) This mirror produces only virtual and erected image.	7) This mirror produces both real and virtual images depending upon position of object.
8) In this mirror m is – ve, v and f are + ve.	8) In this mirror u, v and f are –ve. But when object is placed between F and P then u and f are –ve, v is + ve.
9) These mirrors are used as rear view mirrors for vehicles.	9) These mirrors are used in telescopes and used as reflectors in headlights of vehicles.

3. Distinguish between real and virtual images.

Ans :

Real Image	Virtual Image
1) The image which is caught by a screen is called real image.	1) The image which could not be caught by the screen is called virtual image.
2) In this the rays actually meet at the image point.	2) In this the rays appear to diverge from the image point.
3) It is always inverted.	3) It is always erect.
4) It is formed by concave mirror/convex lens.	4) It is formed by convex mirror/plane mirror/concave mirror/concave lens.
5) Image formed by actual intersection of reflected rays is real image.	5) Image formed by meeting the extended reflected rays is virtual image

4. How do you get a virtual image using a concave mirror?

Ans: We can get a virtual image using concave mirror by placing the object in between

P and F.

(or)

5. What do you know about the terms given below related to the spherical mirrors?

a) Pole b) Centre of curvature c) Focus d) Radius of curvature e) Focal length

f) Principal axis g) Object distance h) Image distance i) Magnification

Ans: a) Pole : The mid point (Geometrical centre) of the mirror is called pole (P) of the mirror.

b) Centre of curvature : The centre of the sphere of which the mirror forms a part is called centre of curvature. It is denoted by 'C'.

c) Focus : A point on the principal axis where a beam of light parallel to the principal axis either converges into or appears to diverge from after reflection from the mirror is called focus (or) focal point (F).

d) Radius of curvature : The radius of the sphere of which the mirror forms a part is called radius of curvature (or)

The distance between pole and centre of curvature of the spherical mirror is known as radius of curvature. It is denoted by 'R'.

e) Focal length : The distance of the focus from the pole is called the focal length (f) of the mirror.

f) Principal axis : The line joining the pole and the centre of curvature is called the principal axis.

g) Object distance : The distance of the object from the pole is known as object distance (u).

h) Image distance : The distance of the image from the pole is known as image distance (v).

i) Magnification : The ratio of size of image to the size of object is known as magnification.

Magnification (m) =

In all the cases of spherical mirror the magnification factor is equal to

m =

6. What do you infer from the experiment which you did to measure the object distance and image distance ?

Ans: I observed the following points from the experiment with concave mirrors, to form images at different places, they are :

1) As the object moves from infinity to 'F' of the concave mirror, the image distance increases.

2) As the object distance decreases from 'F' to 'P' image distance also decreases.

II. APPLICATION OF CONCEPTS :

1. Find the distance of the image, when an object is placed on the principal axis at a distance of 10 cm in front of a concave mirror whose radius of curvature is 8 cm.

Ans: Object distance u = – 10 cm

Radius of curvature (R) = – 8 cm

Focal length f =

= – 4 cm

Image distance v = ?

Mirror formula :

⇒ =

⇒ v =

⇒ – 6.67 cm

The image distance = 6.7 cm. (infront of the mirror)

i.e., Real and inverted image is formed at same side of the object.

2. The magnification product by a mirror is +1. What does it mean ?

Ans: 1) Magnification is ratio of size of image to size of object. A mirror’s magnification is + 1 means size of image and object are same for a mirror and image is virtual and erect.

2) The magnification produced by a plane mirror will be + 1, but produced by a curved mirror will not be + 1.

3. If the spherical mirrors were not known to human beings, guess the consequences.

Ans: 1) Spherical (convex) mirrors will create a rear view mirror in automobiles.

2) Spherical mirror (concave) will diverge the light rays over large area. Hence it is used as reflector for street light bulbs.

3) Examining the backside of tooth by dentists made easy by concave mirrors.

4) Observing the traffic from the backside of a vehicle is possible with convex mirrors.

5) Solar heaters/cookers are manufactured using the principle of concave mirrors.

If spherical mirrors were not known to human beings, the above said developments may not be possible.

4. Draw suitable rays by which we can guess the position of the image formed by a concave mirror.

Ans:

5. Show the formation of image with a ray diagram, when an object is placed on the principal axis of a concave mirror away from the centre of curvature.

Ans: When the object is placed away from the centre of curvature on the principal axis, the image will form between C and F.

6. Why do we prefer a convex mirror as a rear-view mirror in the vehicles?

Ans: 1) Convex mirror always gives an erect and diminished image.

2) The image distance will be smaller than the object distance.

3) A convex mirror has a wider field of view than a plane mirror.

Hence we prefer convex mirror as rear-view mirror in the vehicles, as we have to observe the vehicles which are at the back of our vehicle.

III. HIGHER ORDER THINKING QUESTIONS :

1. A convex mirror with a radius of curvature of 3 m is used as rear view mirror for a vehicle. If a bus is located at 5 m from this mirror, find the position, nature and size of the image.

Ans : Given, R = + 3 m (for convex mirror) ; f =3/2 = 1.5 m ; u = – 5 m ; v = ?

The mirror formula is

⇒

⇒ v =

The image is virtual seen in the mirror.

Magnification, m =

= 0.23

Position = 1.15 m behind the mirror

Nature = Virtual and erected.

Image is erect and smaller in size by a factor of 0.23.

2. To form the image on the object itself, how should we place the object in front of a concave mirror? Explain with a ray diagram.

Ans: 1) When the object is kept at centre of curvature of a concave mirror, the image will form at the centre of curvature but either side of the principal axis.

2) So, to form the image on object itself, the object should be placed in such a way that principal axis should pass through the geometrical centre of the object. Then half of the part of the object will be above the principal axis and the other half will be below the principal axis. We get the image also at same place that means on the object itself but inverted.