In an experiment with convex lens of focal length f, the screen is fixed at a distance D from the object. A student slowly moves the lens away from…

In an experiment with convex lens of focal length f, the screen is fixed at a distance D from the object. A student slowly moves the lens away from the object towards the screen and finds that she is able to form sharp image of the object for two positions of the lens. The distance between these two positions of the lens is d.

The value of d is

$\displaystyle \sqrt{\mathrm{D}(\mathrm{D}-4 \mathrm{f})}$

$\displaystyle \sqrt{\mathrm{D}(\mathrm{D}-2 \mathrm{f})}$

$\displaystyle 2 \sqrt{\mathrm{Df}}$

$\displaystyle \sqrt{\mathrm{D}(\mathrm{D}-\mathrm{f})}$

Compared to the size of the object, the images formed in the two positions of the lens are respectively

reduced, enlarged

reduced, reduced

enlarged, enlarged

enlarged, reduced

If the distance between object and screen is $\displaystyle 80.00$ cm and the lens forms sharp images at two positions separated by $\displaystyle 20.00$ cm., the focal length of convex lens is

15.$\displaystyle 50$ cm

18.$\displaystyle 75$ cm

20.$\displaystyle 50$ cm

22.$\displaystyle 75$ cm

Consider a convex lens of focal length $\displaystyle 15$ cms. For which of the following values of object-screen distance, two positions of the object can be found to obtain sharp image on the screen ?

$\displaystyle 45$ cm

$\displaystyle 50$ cm

$\displaystyle 55$ cm

$\displaystyle 65$ cm

A thin convex lens of focal length $\displaystyle 10$ cm and another thin lens of focal length 'f' are placed coaxially in contact. If the power of their combination is $\displaystyle \frac{10}{3} \mathrm{D}$, the value of ' f ' is

-$\displaystyle 15$ cm

-$\displaystyle 10$ cm

-$\displaystyle 20$ cm

-$\displaystyle 30$ cm