Question

An object is placed in front of two convex lenses
one by one at a distance u from the lens. The focal
lengths of the lenses are 30 cm and 15 cm
respectively. If the size of image formed in the two
cases is same, then u is
(1) 15 cm
(2) 20 cm
(3) 25 cm
(4) 30 cm
future of t​

Answer 1

Answer:22.5

Explanation:25+15+30+20= 90

90÷4=22.5

Answer 2

Option (b) 20 cm.

Explanation:

The magnification for the lens is given by

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

Here u is the object distance from lens and f is the focal length of the lens.

Since an object is placed in front of two convex lenses one by one at a distance u from the lens, therefore

$m_1=\frac{f_1}{f_1-u}$

and

$m_2=\frac{f_2}{f_2-u}$

As the size of image formed in the two  cases is same, then magnifications are equal,

$m_1=m_2$

Given  $f_1=30 cm,f_2=15cm$

Substitute the values, we get

$\frac{30}{30-u} =\frac{15}{15-u}$

$30(15-u)=15(30-u)$

u = 0 which inconsistent.

So we take

$|m_1|=|m_2|$

$|\frac{30}{30-u}| =|\frac{15}{15-u}|$

$|\frac{30}{30-u}| =|\frac{15}{u-15}|$

u =20 cm.

Thus the value of u is 20 cm.

#Learn More: magnification

https://brainly.in/question/7856260