Question: Q. 4. Use the mirror equation to show that:
(i) An object placed between $f$ and $2 f$ of a concave mirror produces a real image beyond $2 f$.
(ii) a convex mirror always produces a virtual image independent of the location of the object.
(iii) an object placed between the pole and the focus of a concave mirror produces a virtual and enlarged image.
A[OD 2011]
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Solution:
Ans. (i) Try yourself Similar Q. 1 Short Answer Type Questions-I
(ii) Try yourself Similar Q. 2 (ii) Short Answer Type Questions-II
(iii) Using mirror formula
$$ \frac{1}{v}+\frac{1}{u}=\frac{1}{f} $$
For concave mirror,
$$ \begin{array}{llrl} & f & \frac{1}{v}+\frac{1}{u} & <0 \ & & \frac{1}{v}-\frac{1}{u} & <0 \ \therefore & \frac{1}{v} & <\frac{1}{u} \end{array} $$
$v>u$ as $v$ is always positive so image is virtual.
Now, $m=\left|\frac{v}{u}\right|>1$, Hence image is always enlarged. 1
Commonly Made Error
- Many candidates made lengthy calculations, which were not required. In some cases they started with correct formula, but did wrongly sign conversions in between.
