Power and Thin Lenses in Contact

Q. Two similar thin equiconvex lenses of focal length $f$ each are kept coaxially in contact with each other such that the focal length of the combination is $F_1$. When the space between the two lenses is filled with glycerin (which has the same refractive index $\left(\mu =1.5\right)$ as that of lens, the equivalent focal length is $F_2$. The ratio $F_1:F_2$ will be

1. 2 : 1
2. 1 : 2
3. 2 : 3
4. 3 : 4

Q. A convex lens is placed in contact with a mirror as shown. If the space between them is filled with water, its power will

1. decrease
2. increase
3. remain unchanged
4. increase or decrease depending on the focal length.

Q. A lens of power $+2.0\text{D}$ is placed in contact with another of power $-1.0\text{D}$. The combination will behave like

1. A converging lens of focal length $100\text{cm}$
2. A diverging lens of focal length $100\text{cm}$
3. A converging lens of focal length $50\text{cm}$
4. A diverging lens of focal length $50\text{cm}$

Q. A convex lens is in contact with a concave lens. The magnitude of the ratio of their focal lengths is $\frac{2}{3}$. Their equivalent focal length is 30cm. What are their individual focal lengths?

1. -15, 10
2. -10, 15
3. 75, 50
4. -75, 50

Q. A clear transparent glass sphere $(\mu =1.5)$ of radius $R$ is immersed in a liquid of refractive index $1.25$. A parallel beam of light incident on it will converge to a point. The position of this point measured from the centre of the sphere will be

Q. A lens of power + 2 diopters is placed in contact with a lens of power – 1 diopter. The combination will behave like

1. A convergent lens of focal length 50 cm
2. A divergent lens of focal length 100 cm
3. A convergent lens of focal length 100 cm
4. A convergent lens of focal length 200 cm