Optics

Classical Mechanics Level 2

The distance between object and the image formed by concave mirror is 15 cm. The value of transverse magnification is -2. Find the focal length of the mirror.

15 cm 25 cm 40 cm 10 cm

2 solutions

Nelson Mandela
Feb 17, 2015

Given,

v-u (or u-v) = 15cm.

Magnification = -2 = -v/u.

Using sign convention, -2 = -(-v)/-u.

Thus, 2u = v.

So, v>u and so, v-u = 2u-u = u = 15cm.

Then, v = 2u = 2 x 15cm = 30cm.

Using mirror formula (and sign convention).

$\frac { 1 }{ -f } =\frac { 1 }{ -v } +\frac { 1 }{ -u }$ .

= $\frac { 1 }{ f } =\frac { 1 }{ 30 } +\frac { 1 }{ 15 }$ .

Thus, f = 10cm.

Clear cut solution like Mandela. Good.

Muhammad Arifur Rahman - 6 years, 3 months ago

have you gone nuts......... how can focal length of concave mirror be +ve

Mriank Ghosh - 6 years, 3 months ago

The focal length of a concave mirror is negative but the image distance and object distance are also negative. so in the mirror formula, we can cancel all minus.My solution clearly includes that part.The sign convention has been followed.Please read the solution twice before saying its wrong.

Nelson Mandela - 6 years, 3 months ago

Mohamad Zare
Mar 17, 2016

If q/p=m=2,p+q=D=15,so the another formula of concave mirror: f=mD/|m^2-1|=2×15/|4-1|=10

Optics

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