A converging beam of rays is incident on a diverging lens. Having passed through the lens the rays intersect at a point \(15~\text{cm}\) from the lens on the opposite side. If the lens is removed the point where the rays meet will move \(5~\text{cm}\) closer to the lens. The focal length of the lens is:
1.  \(5~\text{cm}\)
2. \(-10~\text{cm}\)
3. \(20~\text{cm}\)
4. \(-30~\text{cm}\)

A lens having focal length \(f\) and aperture of diameter d forms an image of intensity \(I\). An aperture of diameter \(\frac{d}{2}\)in central region of lens is covered by a black paper. The focal length of lens and intensity of the image now will be respectively:
1. \(f\) and \(\frac{I}{4}\)
2.  \(\frac{3f}{4}\) and \(\frac{I}{2}\)
3.  \(f\) and \(\frac{3I}{4}\)
4.  \(\frac{f}{2}\) and \(\frac{I}{2}\)

Two thin lenses of focal lengths f₁ and f₂ are in contact and coaxial. The power of the combination is:

1. $\sqrt{\frac{{\mathrm{f}}_1}{{\mathrm{f}}_2}}$

2. $\sqrt{\frac{{\mathrm{f}}_2}{{\mathrm{f}}_1}}$

3. $\frac{{\mathrm{f}}_1+{\mathrm{f}}_2}{{\mathrm{f}}_1{\mathrm{f}}_2}$

4. None of the above

A boy is trying to start a fire by focusing sunlight on a piece of paper using an equiconvex lens of a focal length of \(10\) cm. The diameter of the sun is \(1.39\times10^9\) m and its mean distance from the earth is \(1.5\times10^{11}\) m. What is the diameter of the sun's image on the paper?
 

A convex lens and a concave lens, each having the same focal length of 25 cm, are put in contact to form a combination of lenses. The power in dioptres of the combination is:

1. 25

2. 50

3. infinite

4. zero