The image formed by a spherical mirror is real, inverted and is of magnification −2. If the image is at a distance of 30 cm from the mirror, where is the object placed? Find the focal length of the mirror. List two characteristics of the image formed if the object is moved 10 cm towards the mirror.

Question

Answer

Given Information:

Image is real and inverted

Magnification, m = -2

Distance between mirror and image, v = -30 cm

Finding Object Distance:

The mirror formula is given by:

1/f = 1/u + 1/v

Where, f is the focal length of the mirror, u is the distance between the mirror and the object, and v is the distance between the mirror and the image.

Substituting the given values in the formula:

1/f = 1/u + (-1/30)

1/f = (u-30)/30u

Using the magnification equation, m = -v/u = -2

Therefore, v = 2u

Substituting this value in the above equation:

1/f = (u-30)/(60u)

Simplifying the equation:

u = 60 cm

Finding Focal Length:

Substituting the value of u in the mirror formula:

1/f = 1/60 + 1/-30

Simplifying the equation:

f = -20 cm

Characteristics of the Image:

The image will be closer to the mirror since the object is moved towards it. Therefore, the distance between the mirror and the image will decrease.

The size of the image will increase since the magnification is -2. As the object moves closer to the mirror, the image will become larger.

Answer

The mirror is concave as the magnification produced is negative.

M=-2

V=30

U=?

M=v/U

M=30/U

-2=30/U

U=30/-2

U=-15

For finding focal length,

1/v+1/u=1/f

1/30+1/-15=1/f

F=-30

The object is placed at a distance of 15 cm in front of the mirror.and the focal length is -30 as the mirror is concave.the image formed will be real and inverted

Similar Class 10 Doubts

The image of an object formed by a mirror is real inverted and is of magnification -1 if the image is at the distance of 30 cm from the mirror where is the object placed find the position of the image if the object is no more 20cm towards the mirror.what is the nature of image obtained ?

The image of an object formed by a lens is of magnification - 1. if the distance between the object and its image is 60 cm what is the focal length of the lens ?if the object is moved 20 CM towards the lens ,where would the image be formed?

Aspherical mirror produces an image of magnification-1 on a screen placed at a distance of 50 cm from the mWitte the type of the mirror.What is the focal length of the mirror?(i) Find the distance of the image for the object. (iv) Draw the ray diagram to show the image formation in tha?

Top Courses for Class 10View all

Science Class 10

Social Studies (SST) Class 10

Mathematics (Maths) Class 10

English Grammar Advanced

English Grammar Basic

Top Courses for Class 10

Top Courses for Class 10

Suggested Free Tests

Related Content

About Class 10

Class 10 Study Material

Class 10 All Subjects

NCERT Textbook Solutions

Other Classes

Important Links

Company