An arrow 2.5 cm high is placed at a distance of 25 cm from a diverging mirror of a focal length of 20 cm. Find the nature, position, and size of the image formed.

By Ritesh|Updated : November 10th, 2022

The image will be formed 11.11 cm behind the mirror, which will be virtual, erect, and 1.11 cm in size. Steps to Find the nature, position, and size of the image formed:

Step 1: Given that

Height of the object: h1 = 2.5 cm

The focal length of the mirror: f = 20 cm

Distance of object from the mirror: u = -25 cm

Step 2: Formula used

The formula 1/f = 1/v + 1/u, where v is the distance between the mirror and the image and u is the distance between the mirror and the object, determines the focal length of the mirror. This is known as the mirror formula.

The formula m = h2/h1 = -v/u, where h2 is the height of the image, h1 is the height of the object, v is the distance of the image from the mirror, and u is the distance of the object from the mirror, yields the magnification.

Step 3: Now we have to find the distance between the image and the object using the mirror formula.

1/20 = 1/v - 1/25

On rearranging we get:

1/v = 1/20 + 1/25

On simplifying we get:

1/v = 9/100

v = 11.11 cm

Step 4: Now we have to find the height of the image

m = h2/h1 = -v/u

h2/2.5 = -11.11/-25

On rearranging we get:

h2 = +1.11 cm

Hence, the image will be formed 11.11 cm behind the mirror, which will be virtual, erect, and 1.11 cm in size.

Summary:

An arrow 2.5 cm high is placed at a distance of 25 cm from a diverging mirror of a focal length of 20 cm. Find the nature, position, and size of the image formed.

An arrow 2.5 cm high is placed at a distance of 25 cm from a diverging mirror of a focal length of 20 cm. The image will be formed at 11.11 cm behind the mirror, which will be virtual, erect, and 1.11 cm in size.

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