A concave spherical mirror has a radius of curvature of 15.0 cm . -Calculate the

Question

A concave spherical mirror has a radius of curvature of 15.0 cm .
-Calculate the location of the image formed by an 10.0-mm-tall object whose distance from the mirror is 15.0 cm .
-Calculate the size of the image. (in mm)
-Calculate the location of the image formed by an 10.0-mm-tall object whose distance from the mirror is 3.75 cm .
-Calculate the size of the image. (in mm)
-Calculate the location of the image formed by an 10.0-mm-tall object whose distance from the mirror is 10.0 m .
-Calculate the size of the image. (in mm)

Explanation / Answer

Given, r= 15cm

f=r/2=15/2= 7.5cm

1.

Use equation,

1/f= 1/do+1/di

1/7.5=1/15+1/di      => di= 15cm

Image distance = 15cm means image is at the center of curvature .

To find image height use equation,

M = hi/ho = - di/do

hi = (- di/do)* ho = (-15/7.5)*10mm = -20mm

Image is inverted and real.

2.

Use equation,

1/f= 1/do+1/di

1/7.5=1/3.75+1/di      => di= -7.5cm

Image distance = -7.5cm means image is 7.5cm behind the mirror.

To find image height use equation,

M = hi/ho = - di/do

hi = (- di/do)* ho = (- (-7.5)/3.75)* 10mm = +20mm

Image is upright and virtual.

3.

Use equation,

1/f= 1/do+1/di

1/7.5=1/10+1/di      => di= 30cm

Image distance = 305cm means image is on the same side of the object .

To find image height use equation,

M = hi/ho = - di/do

hi = (- di/do)* ho = (-30/7.5)*10mm = - 40mm

Image is inverted and real.

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