Question

a) Write down the formula for the magnification obtained by a spherical mirror.
b) Name a mirror that can give an erect and enlarged image of an object.
c) Define the principal focus of a convex mirror.

Answer 1

Hint:
First we will try to understand what magnification is, we know it is a ratio of two identical physical quantities. We will find out which one of the spherical mirrors gives a virtual image. All the rays after reflection tend to bend or actually bends to a point.

Complete step by step solution:

In the given question, we have to answer three parts, relating to spherical mirror:
a. We are asked to write the magnification formula for an image in case of a spherical mirror.
The magnification formula is given by:
\[m = - \dfrac{v}{u}\]
Where,
\[m\] indicates magnification.
\[v\] indicates image distance.
\[u\] indicates object distance.

The magnification formula can also be written as:
\[m = \dfrac{{h'}}{h}\]
Where,
\[m\] indicates magnification.
\[h'\] indicates the height of the image.
\[h\] indicates the height of the object.

Magnification is defined as the enlargement of the image formed by a mirror, whether it is a concave mirror or a convex mirror, relative to the size of the object. The physical size of an object does not change, rather the size of the image changes. Depending on the position of the object placed in front of the mirror, the size of the image varies i.e. it may be enlarged or diminished. Magnification is the idea of the relative size of an image with respect to an image.

b. The mirror which can give an erect and enlarged image of an object is a concave mirror. Concave mirror forms a virtual image, which means the image is formed by the apparent intersection of rays of light after reflection. Virtual images are always erect. In this case, we will get an enlarged and erect image only when the object is placed inside the focus.

c. Principal focus of a convex mirror: It is the focal length of a convex mirror which is present on the other side of the object, where light rays originating from the object, after reflection, appear to meet, but don’t actually meet. A convex mirror always forms a virtual image.


Note:
While answering this question remember that, convex mirror always forms a virtual and erect image, but do remember that the question has asked for the enlarged image too. So, don’t get confused with that. A convex mirror produces a virtual and erect image which is diminished in size. Again, the magnification obtained by a spherical mirror is positive when the image is real and it is negative when the image is virtual.