An object is placed 1m to the left of a lens of focal length of 80 cm. A convex

Question

An object is placed 1m to the left of a lens of focal length of 80 cm. A convex mirror (f=-50cm) is placed one meter to the right of the lens. Locate the final image position. Is it real or virtual? Upright or inverted? If the object is 2 cm tall, how tall is the image? An object is placed 1m to the left of a lens of focal length of 80 cm. A convex mirror (f=-50cm) is placed one meter to the right of the lens. Locate the final image position. Is it real or virtual? Upright or inverted? If the object is 2 cm tall, how tall is the image?

Explanation / Answer

here,

for the lens ,

the object distance, do1 = 100 cm

focal length ,f1 = 80 cm

let the image distance be di1

using the lens formula

1/di1 + 1/do1 = 1/f1

1/100 + 1/di1 = 1/80

di1 = 400 cm

for the mirror

the object distance ,

do2 = 100 - 400 cm   = - 300 cm

focal length , f2 = - 50 cm

let the image distance be di2

using the mirror formula

1/f2 = 1/di2 + 1/do2

- 1/50 = 1/di2 - 1/300

solving for di2

di2 = - 60 cm

the final image position is 60 cm to the left of the mirror

the image is virtual

the image is upright

height of object , ho = 2 cm

the height of image , hi = m * ho

hi = - ( -60/-300) *( -400/100) * 2 cm

hi = - 1.6 cm

the height of image is 1.6 cm

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