Mirror formula

Mirror formula:

If u = object distance, v=image distance and

f = focal length of mirror,then the mirror formula is given by

According to sign conventions we need to assume the distance as follows,

Object distance, u= -ve , Image distance, v = -ve/+ve (depends upon the position of image) and Focal length, f= -ve for concave mirror/+ve for convex mirror.

 

Let’s consider following example to understand this formula more precisely.

Ex.1) An object is kept in front of concave mirror of focal length 20 cm at distance of 15 cm. Find position of image, nature of image.

Solution: Data given ;( using all sign conventions)

Focal length, f= -20 cm

Object distance, u= -15 cm

Image distance=?

Formula:

On substituting the above values, we get

∴ 1/v = 1/(-60)

∴v=-60 cm

Negative value of ‘v’ indicates that image is real but inverted.

Magnification by mirror (M):

Magnification is defined as the ratio of height of image (h2) to the height of object (h1) or the ratio of image distance (v) to object distance (u).

Ex.2) An object of height 10 cm kept in front of converging mirror of focal length 30 cm at distance of 25 cm. Find position of image, nature of image and height of the image.

Solution: Data given ;( using all sign conventions)

Height of object, h1= + 10 cm

Focal length, f= -30 cm

Object distance, u= -25 cm

Image distance=?

Image height=?

Formula:

Negative value of ‘v’ indicates that image is real but inverted.

Now to calculate height of image use 2nd formula

Hence the height of image obtain here will be 60 cm.

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  1. Thank you very much…for this much

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