The lens and mirror in the figure below are separated by 1.00 m and have focal lengths of +79.6 cm and -50.2 cm, respectively

Dolly Robinson

Dolly Robinson

Answered question

2021-03-21

The lens and mirror in the figure below are separated by 1.00 m and have focal lengths of +79.6 cm and -50.2 cm, respectively image

Answer & Explanation

tafzijdeq

tafzijdeq

Skilled2021-03-23Added 92 answers

Let's solve it

image

Jeffrey Jordon

Jeffrey Jordon

Expert2021-09-28Added 2605 answers

The thin lens equation, which links the focal length, image distance, and object distance, is

1p1+1q1=1f1

Rearrange for q1

q1=p1f1p1f1

=(100 cm)(79.6 cm)100 cm79.6 cm

=390 cm

Here, the picture serves as the mirror's subject. Consequently, the mirror's object distance is,

p2=100 cmq1

=100 cm390 cm

=290 cm

The position of the mirror's created image is,

q2=p2f2p2f2

=(290 cm)(50.2 cm)(290 cm(50.2 cm))

=60.7 cm

The final picture is virtual and is 60.7 cm from the mirror, as indicated by the negative sign.

The image's magnification is,

m=(q1p1)(q2p2)

=(390 cm100 cm)(60.7 cm290 cm)

=0.8

The picture appears vertical, which is a good indicator that the magnification is working.

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