Question

A beam of light converges at a point P. A convex
mirror of focal length 12 cm is placed between
the path of the beam such that point P is 2cm
behind the mirror. Now where will the reflected
rays meets or appears to meet from the mirror.​

Answer 1

Answer:

Given: A beam of light converges towards a point O, behind a convex mirror of focal length 10cm.

To find the nature and position of image, if the point O is (i) 5cm behind the mirror (ii) 15cm behind the mirror

Solution:

Case (i): when point O is 5cm behind the mirror

According to the given criteria,

object distance, u=−5cm

focal length, f=−10cm

Applying the mirror formula, we get

f

1

=

v

1

+

u

1

⟹

v

1

=

f

1

−

u

1

⟹

v

1

=

(−10)

1

−

(−5)

1

⟹

v

1

=

10

−1+2

⟹v=10cm

Hence the image is at a distance of 10 cm in-front of the convex mirror.

Magnification, m=−

u

v

=−

(−5)

10

=+2

Nature of the image: virtual, erect and enlarged.

Case (ii): when point O is 15 cm behind the mirror

According to the given criteria,

object distance, u=−15cm

focal length, f=−10cm

Applying the mirror formula, we get

f

1

=

v

1

+

u

1

⟹

v

1

=

f

1

−

u

1

⟹

v

1

=

(−10)

1

−

(−15)

1

⟹

v

1

=

30

−3+2

⟹v=−30cm

Hence the image is at a distance of 30 cm behind the convex mirror.

Magnification, m=−

u

v

=−

(−15)

(−30)

=−2

Nature of the image: Real, inverted and enlarged.