Question

A certain projector uses
a
concave mirror for projecting an
image
object's image on a screen. It
Object
produces an image that is 5 times
bigger than the object and the
screen is 5m away from the
mirror as shown in Fig. 5.2.
i. Give reason why is the image larger than the object? [1]
ii. Calculate the focal length of the mirror,
[2]

Answer 1

Answer:

Answer is 1.25m.

Explanation:

Since image is virtual.

given, u=-5m

v=?

O=?

I=5m

magnifcation (m)=I/O=-5

or, -5=-5/u

or, u=1m.

We Know That,

1/f=1/u+1/v

1/f=1/1-1/5

or, f=1.25m

Answer 2

Answer:

i. The image produced by the concave mirror is larger than the object because of the focusing effect of the mirror. The concave mirror has a curved surface which causes parallel beams of light from the object to focus at one point,which is known as the focal point. The rays of light from the object are reflected by the concave mirror and converge at the focal point. The image of the object is formed at a point which is exactly equal to the focal length away from the mirror. Thus, the image of the object is magnified due to the focusing effect of the mirror.

ii. The focal length, f, of the concave mirror can be calculated by using the formula

1/f = 1/d1+1/d2,

where d1 is the distance between the object and the mirror and

d2 is the distance between the image and the mirror.

In the given case,

d1 = 5m, d2 = 5m.

Substituting these values in the formula,

we get 1/f = 1/5 + 1/5 = 2/5.

Therefore, the focal length of the mirror,

f = 5/2 m.

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