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 lenses are 30cm and 15cm respectively.If the size of image formed in two cases is same,then ‘u’ is-

Answer 1

Answer on Question#55521 - Physics - Optics

An object is placed in front of two convex lenses one by one at a distance ‘u’ from the lens. The focal lengths of lenses are $f_{1} = 30\mathrm{cm}$ and $f_{2} = 15\mathrm{cm}$ respectively. If the size of image formed in two cases is same, then ‘u’ is-

Solution:

The magnification of the object at the object distance $u$ in front of the lens with focal length $f$ is given by

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

It’s given that $|M_1| = |M_2|$, that is

$$\frac {f _ {1}}{| f _ {1} - u |} = \frac {f _ {2}}{| f _ {2} - u |}$$

This equation is equivalent to the following system:

$$\left[ \begin{array}{l} \frac {f _ {1}}{f _ {1} - u} = \frac {f _ {2}}{f _ {2} - u} \\ \frac {f _ {1}}{f _ {1} - u} = \frac {f _ {2}}{u - f _ {2}} \end{array} \right.$$ $$\left[ \begin{array}{l} \frac {3 0 \mathrm {c m}}{3 0 \mathrm {c m} - u} = \frac {1 5 \mathrm {c m}}{1 5 \mathrm {c m} - u} \\ \frac {3 0 \mathrm {c m}}{3 0 \mathrm {c m} - u} = \frac {1 5 \mathrm {c m}}{u - 1 5 \mathrm {c m}} \end{array} \right.$$ $$\left[ \begin{array}{l} 3 0 \mathrm {c m} - 2 u = 3 0 \mathrm {c m} - u \\ 2 u - 3 0 \mathrm {c m} = 3 0 \mathrm {c m} - u \end{array} \right.$$ $$\left[ \begin{array}{l} u = 0 \mathrm {c m} \\ u = 2 0 \mathrm {c m} \end{array} \right.$$

$u = 0\mathrm{cm}$ is inconsistent therefore the answer is $u = 20\mathrm{cm}$.

**Answer:** 20cm.

http://www.AssignmentExpert.com/