Solved Examples on Mirror Equation

1. Find out the position of an object from a convex mirror of the focal length of 6 cm, which produces an image on the mirror axis at 3 cm from the mirror.

Solution:

Given data , f = 6 cm (convex mirror)

v = -3 cm

Using mirror equation, we have

1/u = 1/f-1/v

⇒ 1/u = ⅙ – (-⅓) 

⇒ 1/u = ⅙ + ⅓ = (1+2)/6 = 1/2

⇒ u = 2 cm

Thus, the position of the object is 2 cm from the mirror. 

2. Calculate the focal length of a concave mirror with a curvature radius of 25 cm.  

Solution:

Given that, R = 25 cm (Radius of curvature)

The radius of curvature of a concave mirror is twice its focal length. 

R = 2f

Where R is the radius of curvature of the mirror and F denotes focal length. 

So f = R/2 

Thus, f = 25/2

⇒ f = – 12.5

The negative sign here denotes it’s a concave mirror. 

3. An object is placed at a distance of 2 times of focal length from the pole of the convex mirror, calculate the linear magnification.

Solution:

Let the Focal length of mirror = f

So, the object distance, u = -2f 

The formula to calculate image distance we use mirror formula as,

1 / v + 1 / u = 1 / f

Therefore,

1 / v + 1 / -2f = 1 / f 

⇒ 1 / v  = 1 / f + 1 / 2f  

⇒ 1 / v  = 3 / 2f

⇒ v = 2f / 3

Magnification is given as, 

m = – v / u

⇒ m = -(2f/3) / (-2f) 

⇒ m =  1/3

4. If the image is a distance of 6 cm and the object is at 12 cm in the front of the concave mirror, calculate the magnification formed.

Solution:

Given that,

The distance of object, u = – 12 cm

The distance of image, v = – 6 cm

Since,

Magnification is given by, 

m = – v / u

⇒ m = – (-6 / -12) 

⇒ m = -0.5

Hence, the image will be diminished by nearly half as size of object. 
 

5. Calculate the image’s position if the bus is 5 m away from a convex mirror. The Convex Mirror has a 8 m radius of curvature. 

Solution:

Given that,

The curvature radius (R) is +8.00 m.

Distance between objects (u) = -5.00 m

We need to figure out what image distance(v) equals.

We know that f = R/2 = 8/2 = 4 m 

The mirror’s formula is 1/u + 1/v = 1/f

⇒ 1/v = 1/f – 1/u

⇒ 1/v = 1/4 – 1/(-5)

⇒ 1/v = 9/20

Thus, v = 20/9

2.22 meters ()

As a result, the picture is created 2.22 meters away from the mirror.

Mirror Equation in Physics is the equation for mirrors that provides the relation between the distance of the object and the image, as well as its focal length. Mirror Equation is helpful in determining object position, image position or focal length given that two of the parameters are given. In optics, which is the branch of science that deals with the study of light and its interactions with various materials and optical elements, mirrors are used in various instruments for various purposes. Thus, understanding the relationship between the focal length of the mirror and the distance between the object and the image from the mirror is very important.

In this article, we will explore the concept of the Mirror Equation in detail, Mirror Equation Proof, and Mirror Equation for Magnification with various types of mirrors as well. So, let’s start learning about the concept of Mirror Equations.