Several different combinations of mirrors and objects are given. Find the image

Question

Several different combinations of mirrors and objects are given. Find the image location and the linear magnification for each mirror/object combination given. Also state whether the mirror is concave, convex, or plane for each.

a) The object is located a distance 100 cm from the mirror and the mirror has a focal length of 25 cm. What is the image location? i = ?cm

b) The object is located a distance 100 cm from the mirror and the mirror has a focal length of 25 cm. What is the linear magnification? m = ?

c) The object is located a distance 100 cm from the mirror and the mirror has a focal length of 25 cm. Is the mirror concave, convex or plane?

d) The object is located at the focal distance in front of a mirror which has f = -25 cm. What is the image location? i = ?cm

Explanation / Answer

a)

here

u = 100 cm

f = 25 cm

the mirror formula is

1 / f = 1 / v +1/u

1 / v = 1 / f - 1 /u

1 / v = 1 / 25 - 1 / 100

v = 33.3 cm

the image distance is 33.3 cm

b)

then the magnification is

m = - v / u

m = - 33.3 / 100 = -0.33

the magnification of the mirror is -0.33

c)

the mirror is concave mirror

d)

when f = -25 cm

u = -25 cm

then by using the mirror formula

1 / f = 1 / v + 1 / u

1 / v = 1 / f - 1 / u

1 / v = 1 / -25 - 1 / -25

v = 1 / 0

v = infinity

so the image will formed at infinity

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