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Question

An object 5.0 cm in length is placed at a distance of 20 cm in front of a convex mirror with a radius of curvature of 30 cm. Find the position of the image, its nature, and size.


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Solution

Step1: Given data

The radius of curvature (R) of the mirror =30cm

Focal length, f=R2=302=15cm

Distance of the object, u=-20cm

Height of the object, h=5cm

Step 2: Finding the distance of the image (v) using the formula

1v+1u=1f1v=1f-1u1v=115-1-20v=8.57cm

Image is virtual and erect and formed behind the mirror.

Step 3: Finding the size of the image using the formula of magnification

m=-vu=hiho=HeightofimageHeightofobjecthi5=8.5720=0.428hi=0.428x5=2.14cm

Position of Image: Behind the mirror.

Nature of Image: Virtual and Erect.

Size of the Image: Diminished.


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