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.

By Ritesh|Updated : November 3rd, 2022

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. The position of the image is behind the mirror, its nature is virtual and erect and its size is diminished.

Step1: Given the data

Focal length, f = R/2 = 30/2 = 15 cm

Distance of the object, u = - 20 cm

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

Height of the object, h = 5 cm

Step 2: Using the formula, we can determine the image's (v) distance.

1/v + 1/u = 1/f

1/v = 1/f - 1/u

1/v = 1/15 - 1/-20

v = 8.57 cm

A virtual, upright image is created behind the mirror.

Step 3: Now by using the magnification formula, we can determine the image's size

The formula is given by,

m = -v/u = hi/ho = Height of image/ Height of object

hi/5 = 8.57/20 = 0.428

hi = 0.428 x 5 = 2.14 cm

Image position: behind the mirror.

Virtual and upright in nature.

The image's size has decreased.

Summary:

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.

A convex mirror with a radius of curvature of 30 cm is in front of an object with a length of 5.0 cm at a distance of 20 cm. The position of the image is behind the mirror; it is virtual and erect in character, with a reduced size.

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