Combinations of Lenses & Mirrors

Q. A convex lens A of focal length 20 cm and a concave lens B of focal length 5 cm are kept along the same axis with the distance d between them. If a parallel beam of light falling on A leaves B as a parallel beam, then distance d in cm will be

1. 25
2. 15
3. 30
4. 50

Q. A concave mirror of focal length $10cm$ and convex mirror of focal length $15cm$ are placed facing each other $40cm$ apart. A point object is placed between the mirrors on their common axis and $15cm$ from the concave mirror. One of the images is produced by the reflection first at concave mirror and then at convex mirror. The distance of this image from convex mirror is

1. $6cm$
2. $5cm$
3. $4cm$
4. $3cm$

Q. A luminous object is placed at a distance of 30 cm from the convex lens of focal length 20 cm. On the other side of the lens, at what distance from the lens a convex mirror of radius of curvature 10 cm be placed in order to have an upright image of the object coincident with it

1. 12 cm
2. 30 cm
3. 50 cm
4. 60 cm

Q. A combination of two thin lenses with focal lengths $f_1$ and $f_2$ respectively forms an image of distant object at distance 60 cm when lenses are in contact. The position of this image shifts by 30 cm towards the combination when two lenses are separated by 10 cm. The corresponding values of $f_1$ and $f_2$ are

1. 30 cm, - 60 cm
2. 20 cm, - 30 cm
3. 15 cm, - 20 cm
4. 12 cm, – 15 cm

Q. An eye specialist prescribes spectacles having combination of convex lens of focal length $40\text{cm}$ in contact with a concave lens of focal length $25\text{cm}$. The power of this lens combination in diopters is

1. $+1.5$
2. $-1.5$
3. $+6.67$
4. $-6.67$

Q. A plano convex lens fits exactly into a plano concave lens. Their plane surface are parallel to each other. If the refractive indices are ${\mu }_1$ and ${\mu }_2$ and R is the radius of curvature the focal length of the combination is

1. $\frac{R}{{\mu }_1-{\mu }_2}$
2. $\frac{2R}{{\mu }_2-{\mu }_1}$
3. $\frac{R}{2({\mu }_1-{\mu }_2)}$
4. $\frac{R}{2-({\mu }_1-{\mu }_2)}$

Q. A convex lens is cut in half along its principal axis and the two halves are separated by a distance of $12\text{cm}$. An object is placed $6\text{cm}$ in front of the lens as shown in Figure. Two sharp images are formed on the screen placed $80\text{cm}$ from the object. What is the focal length of the lens ?

1. $12.50\text{cm}$
2. $23.45\text{cm}$
3. $17.30\text{cm}$
4. $19.55\text{cm}$

Q. In the situation shown in the figure, three lenses of focal lengths $20\text{cm},30\text{cm}$ and $36\text{cm}$ are held coaxial such that separation between first and second lens is $12\text{cm}$ and between second and third lens is $10\text{cm}$. If the final image of an object at a distance of $30\text{cm}$ from first lens is at a distance $10x\text{cm}$ from the middle lens, then find the value of $x$.

Q.

A point object is kept in air at $40\text{cm}$ in front of an equiconvex lens silvered on one side. Radius of curvature of each side of lens is $20\text{cm}$ and refractive index of lens material is $3/2$. Where is the final image formed from silvered lens?

1. $60\text{cm}$
2. $\frac{30}{7}\text{cm}$
3. $90\text{cm}$
4. $\frac{40}{7}\text{cm}$

Q. A convex lens of refractive index $\frac{3}{2}$ has a power of $2.5\text{D}$ in air. If it is placed in a liquid of refractive index $2$, then the new power of the lens is

1. $1.5\text{D}$
2. $1.2\text{D}$
3. $-1.25\text{D}$
4. $1.25\text{D}$

Q. Calculate the length of the tube of a simple microscope, if objective and eyepiece focal lengths are $0.5\text{cm}$ and $4\text{cm}$. Given that, the magnifying power of a relaxed eye is $30$.

1. $3.5\text{cm}$
2. $7\text{cm}$
3. $14\text{cm}$
4. $9\text{cm}$

Q. A convex lens is cut in half along its principal axis and the two halves are separated by a distance of $12\text{cm}$. An object is placed at a distance of $6\text{cm}$ in front of one lens as shown in figure. Two sharp images are formed on the screen placed $80\text{cm}$ from the object. What is the focal length of the lens ?

1. $19.5\text{cm}$
2. $12\text{cm}$
3. $0.6\text{cm}$
4. $16.5\text{cm}$

Q. Consider a concave mirror and a convex lens (refractive index = 1.5) of focal length $10\text{cm}$ each, separated by a distance of $50\text{cm}$ in air as shown in the figure. An object is placed at a distance of $15\text{cm}$ from the mirror. Its erect image formed by this combination has magnification $M_1$.When the set up is kept in a medium of refractive index $\frac{7}{6}$, the magnification becomes $M_2$. The magnitude of $\left|\frac{M_2}{M_1}\right|$ is

Q. A plano convex lens fits exactly into a plano concave lens. Their plane surface are parallel to each other. If the refractive indices are ${\mu }_1$ and ${\mu }_2$ and R is the radius of curvature the focal length of the combination is

1. $\frac{R}{{\mu }_1-{\mu }_2}$
2. $\frac{2R}{{\mu }_2-{\mu }_1}$
3. $\frac{R}{2({\mu }_1-{\mu }_2)}$
4. $\frac{R}{2-({\mu }_1-{\mu }_2)}$

Q. A biconvex lens has a focal length of $10$ cm. It is cut in half and two pieces are placed as shown. The focal length of the final combination in cm is

1. $10$
2. $20$
3. $40$
4. Not a lens

Q. Calculate the length of the tube of a simple microscope, if objective and eyepiece focal lengths are $0.5\text{cm}$ and $4\text{cm}$. Given that, the magnifying power of a relaxed eye is $30$.

1. $9\text{cm}$
2. $7\text{cm}$
3. $3.5\text{cm}$
4. $14\text{cm}$