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Solved Examples on Sign Conventions for Spherical Mirrors

Magnification (or Linear magnification)

Sign Conventions for Spherical Mirrors – FAQs

Example 1: A concave mirror produces two times magnified real image of an object placed 10 cm in front of it. Find the position of the image.

Solution: 

Here, -10 cm (Sign convention) 

m = – 2 ( Image is real). 

But m =-v/u   

-2=-v/u

v=-20 cm

Thus, image of the object is at 20 cm from the pole of the mirror and in front of the mirror. 

Example 2: An object of 5 cm in size is placed at a distance of 20 cm from its concave minor of the focal length of 15 cm At what distance from the mirror, should a screen be placed to get the sharp image? Also, calculate the size of the image. 

Solution: 

Given that,

h=+5 cm 

f = – 15.0 cm          (Sign convention) 

u = – 20 cm           (Sign convention) 

Determination of the position of image. 

Using, 

1/u + 1/v =1/f 

We get , 

1/v = 1/f-1/u

v = -60cm

So the screen must be placed at a distance of 60 cm in front of the concave mirror. 

Determination of size of the image and its nature.

Using, 

m= h’/h =-v/u

 h‘=-(v/u)h

= -15 cm

Thus, the size of image -15cm, negative sign with h’ shows that the image is real and inverted. 

Example 3: A convex mirror used in a bus has a radius of curvature of 3.5 m. If the driver of the bus locates a car 10 m behind the bus, find the position, nature, and size of the image of the car.

Solution:  

Here, R = 3-5 m f = R 2 3-5 2 = 1.75m, u = – 100 m. 

Determination of the position of the car. 

Using, Using, 1/u + 1/v =1/f 

 1/v =1/f -1/u

 1/v= 1/1.75 -1/(-10)  

v = 1.5 m

Thus, the car appears to be at 1.5 m from the convex mirror and behind the mirror. 

Determination of the size and nature of the image 

Using, m= h’/h =-v/u

= -1.5/-10

= 0.15

Thus, the size of the image of the car is 0.15 times the actual size of the car. 

Since m is positive, so image of the car is virtual and erect (i.e., upright).

Example 4: Determine the focal length of the concave mirror given the radius of curvature is 20 cm.

Solution:

Given that,

The radius of curvature of the mirror, R is 20 cm.

Using the formula,

R = f/2

or 

f = R × 2

= 20 cm × 2

= 40 cm

Hence, the focal length of the mirror is 40 cm.

Related Articles:

Sign Convention for Spherical Mirrors

Sign Convention for Spherical Mirrors: While studying the reflection of light by spherical mirrors and the formation of images by spherical mirrors, a set of sign conventions are needed to learn that is required to measure the focal length, the distance of the object or image from the mirror, and the magnification of the mirror.

Before, understanding the concept of sign conventions for spherical mirrors first discuss some commonly used terms in a spherical mirror.

Table of Content

  • Commonly Used Terms in Spherical Mirrors
  • Sign Convention for Spherical Mirrors
  • Important Points to Remember
  • Mirror Formula 
  • Magnification (or Linear magnification)
  • Solved Examples on Sign Conventions for Spherical Mirrors

Similar Reads

Commonly Used Terms in Spherical Mirrors

...

Sign Convention for Spherical Mirrors

The set of guidelines to set signs for image distance, object distance, focal length, etc for mathematical calculation during an image formation is called the Sign Convention. The sign conventions in the case of the spherical mirrors are made in taking into consideration that the objects are always placed on the left side of the mirror, such that the direction of incident light is from left to right....

Important Points to Remember

According to the sign convention, the distances towards the left of the mirror are negative. Since an object is always placed to the left side of a mirror, therefore, the object distance (u) is always negative. The images formed by a concave mirror can be either behind the mirror (virtual) or in front of the mirror (real). So, the image distance (v) for a concave mirror can be either positive or negative depending on the position of the image. If the image is formed behind a concave mirror, the image distance (v) is positive but if the image is formed in front of the mirror, then the image distance will be negative. In a convex mirror, the image is always formed on the right-hand side (behind the mirror), so the image distance (o) for a convex mirror will be always positive. The focus of a concave mirror is in front of the mirror on the left side, so the focal length of a concave mirror will be negative (and written with a minus sign, say, -10 cm). On the other hand, the focus of the convex mirror is behind the mirror on the right side, so the focal length (and written with a plus sign, say +20 cm or just 20 cm), of a convex mirror is positive. The Focal Length and radius of curvature of a concave mirror are taken negatively. The Focal Length and radius of curvature of a convex mirror are taken positively....

Mirror Formula

The distance of the position of an object on the principal axis from the pole of a spherical mirror is known as object distance. It is denoted by u. The distance of the position of the image of an object on the principal axis from the pole of a spherical mirror is known as the image distance. It is denoted by v....

Magnification (or Linear magnification)

Linear Magnification produced by a mirror is defined as the ratio of the size (or height) of the image to the size (or height) of the object. It is denoted by m. If h’ is the size (or height) of the image produced by the mirror and h is the size (or height) of the object....

Solved Examples on Sign Conventions for Spherical Mirrors

Example 1: A concave mirror produces two times magnified real image of an object placed 10 cm in front of it. Find the position of the image....

Sign Conventions for Spherical Mirrors – FAQs

What is the function of a Convex Mirror?...

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Magnification (or Linear magnification)

Sign Conventions for Spherical Mirrors – FAQs