Question

If a lens is moved towards the object from a distance of 40 cm to 30 cm, the magnification of the image remains the same (numarically). The focal length of the lens is
(1) 20 cm
(2) 15 cm
(3) 35 cm
(4) 18 cm​

Answer 1

Answer:

Answer for the above question is (3) - 35 cm

Answer 2

(3) 35 cm

Step by step explanation:

As we know, magnification can be written as,

$m=\frac{f}{u+f}$

where f is the focal length

and u is the object distance.

According to the question,

$u_1=-40 \ cm\\u_2= -30\ cm$

$|m_1|=|m_2|$

$\implies |\frac{f}{-40+f}|= |\frac{f}{-30+f}|$

if m has same sign then,

$\frac{f}{-40+f} =\frac{f}{-30+f} \\\\\implies -40+f=-30+f$, which is impossible.

if m has the opposite sign then,

$\frac{f}{-40+f} =\frac{-f}{-30+f} \\\\\implies -40+f=30-f\\\\\implies 2f=70\\\\\implies f=35 \ cm$

Hence the required focal length is 35 cm.

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