(a) We know that convex mirror is used in security mirrors :
According to the question :
Customer is standing at a distance of 20m (object distance) and radius of curvature of mirror is 5m
Given,
Radius of curvature, R=+5m
Object distance, u=−20m
Image distance, v= ?
Height of image, h′= ?
Focal length, f=‌

R

2

=+‌

5

2

Since, ‌

1

v

+‌

1

u

=‌

1

f

or
‌

1

f

=‌

2

5

or ‌

1

v

=‌

1

f

−‌

1

u

‌=‌

2

5

+‌

1

20

‌=‌

8+1

20

=‌

9

20

⇒‌‌‌

1

v

‌=‌

9

20

⇒‌‌v‌=‌

20

9

=+2.22m
The image is 2.22m at the back of minor
Magnification,
‌m=‌

h′

h

=−‌

v

u

‌=−‌

2.22

−20

=+0.11
The image is virtual, erect of smaller in size by a factor of 0.11 .
(b) Concave mirrors are commonly used in torches, search-lights and vehicles headlights to get powerful parallel beams of light. The dentists use concave mirrors to see large images of the teeth of patients.
OR
(i) The nature of lens used for this purpose is convex lens because it produces a magnified image of the palm.
(ii) There are two cases for which a real and magnified image of object is obtained in convex lens :
(a) When the object is placed at focus of the lens.
(b) When the object is placed between focus and centre of curvature of the lens.
(iii) Given,
f‌=10‌cm
u‌=−5‌cm
We know,

1

f

‌=‌

1

v

−‌

1

u

⇒‌‌

1

10

‌=‌

1

v

−‌

1

−5

⇒‌‌‌

1

10

‌=‌

1

v

+‌

1

5

⇒‌

1

v

‌=‌

1

10

−‌

1

5

⇒‌

1

v

‌=‌

1−2

10

⇒‌

1

v

‌=‌

−1

10

‌v‌=−10‌cm
The image is formed 10‌cm away from the lens on the same side of the object and would be enlarged, virtual and erect.
m=‌

hi

ho

=‌

v

u

=‌

10

−5

=−2
∴ Size of image is 2 times larger the size of object.