Convex Mirror: Overview, Questions, Preparation

A convex mirror is a curved or spherical mirror in which the reflective surface bulges out towards the source of the light. Instead of using it to focus light, the bulging out surface reflects light outwards. Since the cut portion of the hollow sphere is painted from inside, its outer surface assumes the role of a reflecting surface. 

The convex mirror diagram shown in the image above has a point called the centre of curvature (C), which represents the centre of the original sphere and the principal axis, which is a line that passes from the mirror’s surface to the sphere’s centre. There is also a focal point (F) on the mirror, located along the principal axis, which is situated midway between the mirror’s surface and the centre of curvature. The mirror’s side on which the focal point and the centre of curvature are located is opposite to the object. Since the focal point is placed behind the convex mirror, it is said to have a negative focal length value.

With respect to the position of the object in a convex mirror, two types of image formation are possible.

• When the object is situated at infinity.
• When the object is situated between the pole and infinity (i.e. at a finite distance from the mirror).  

When the object is situated at infinity

The possibility, in which the object is placed at infinity, a point size image is formed at the principal focus, which is a place behind the convex mirror. The image that is formed is highly diminished, erect, and virtual.

When the object is situated between pole and infinity (i.e. at a finite distance from the mirror)

In a convex mirror, when the object is placed between the pole and infinity (i.e. at a finite distance from the mirror), a diminished, virtual, and erect image is formed, which is also behind the convex mirror, but between the focus (F) and the pole (P).  

This concept is taught under the chapter Light — Reflection and Refraction in class 10. The weightage of this chapter is 7 marks. The concept of convex mirrors bears importance in classes 11 and 12 too.

• A 5 cm high object is positioned perpendicular to the main axis of a 20 cm focal length convex lens. The width between the object and the lens is 30 cm. Find v.

Solution:

u=−30  cm

f=20  cm, 

Using the lens formula  1/f = 1/v−1/u 

1/v = 1/u+1/f

= 1/−30+1/20

= −2+3/60= 1/60   

1/v = 160 

v= 60cm

• A 5cm high object is positioned perpendicular to the main axis of a convex lens with a focal length of 10 cm. The width between the object and the lens is 15 cm. Find the nature, position, magnification and size of the image. 

Solution:

1/f = 1/v−1/u

1/10 = 1/v−(1/−15)

v= 30cm

m = v/u=−2

hi/ho = −2

hi= −10cm

• A 10 cm high object is positioned perpendicular to the main axis of a convex lens with a focal length of 30 cm. The distance between the object and the lens is 20 cm. Find v.

Solution:

1/f = 1/v−(1/u)

1/30 = 1/v−(1/−20)

v = −60 cm

Q: What are the uses of convex mirrors?

Q: Differentiate between a concave and a convex mirror.

Q: Why is a convex mirror called a diverging mirror?

Q: What type of image is formed by a convex mirror?

Q: Why can a convex mirror not form a real image?