Question

A convex mirror used for rear-view on an automobile has a radius of curvature of 4.00 m. If a bus is located at 5.00 m from this mirror, the size of the image will be: (Ask)




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Answer 1

Given:-

• Radius of Curvature ,R = 4m

• Object Distance ,u = 5m

To Find:-

• Image distance ,v

• Height of image ,hi

Solution:-

As we know that the relationship between Radius of Curvature and Focal length .

• f = R/2

Substitute the value we get

→ f = 4/2 = 2 m

Now, Calculating the image distance using mirror formula.

• 1/v + 1/u = 1/f

where,

v is the Image Position

u is the object distance

f is the focal length

Substitute the value we get

→ 1/v = 1/f - 1/u

→ 1/v = 1/2 -1/(-5)

→ 1/v = 1/2 + 1/5

→ 1/v = 5+2/10

→ 1/v = 7/10

→ v = 10/7

→ v = 1.42 m

Therefore,the image distance is 1.42 m at the back of mirror.

Now,

magnification ,m = hi/ho = -v/u

substitute the value we get

→ hi/ho = -1.42/-5

→ hi/ho = 1.42/5

→ hi/ho = 0.28

→ hi = 0.28 ho

The image is virtual , erect and smaller in size and height of image is 0.28 m .