Lens Maker's Formula

Q.

Name the type of mirror used in the following situations.

(a) Headlights of a car

(b) Side/rear-view mirror of a vehicle

(c) Solar furnace

Support your answer with reason.

Q.

A doctor has prescribed a corrective lens of power $+1.5D$. Find the focal length of the lens. Is the prescribed lens diverging or converging?

Q.

What happens to the focal length of a convex lens when it is immersed in water?

Q.

How do you find the slit width of a double slit?

Q. Diameter of a plano–convex lens is 6 cm and thickness at the centre is 3 mm. If the speed of light in the material of the lens is 2 10⁸ m/sec, the focal length of the lens is

1. 30 cm
2. 20 cm
3. 10 cm
4. 15 cm

Q. A convex lens of power $4\text{D}$ is placed at a distance of $40\text{cm}$ from a wall. At what distance from the lens should a candle be placed so that its image is formed on the wall?

1. $\frac{100}{3}\text{cm}$
2. $\frac{200}{3}\text{cm}$
3. $\frac{500}{3}\text{cm}$
4. $\frac{700}{3}\text{cm}$

Q. Two coherent point sources $S_1$ and $S_2$ vibrating in phase emit light of wavelength $\lambda$. The separation between the sources is $2\lambda$. Consider a line passing through $S_2$ and perpendicular to the line $S_1{S}_2$. Find the position of nearest minima.

1. $D=\frac{\lambda }{2}$
   
2. $D=\frac{5\lambda }{12}$
   
3. $D=\frac{7\lambda }{12}$
   
4. $D=\frac{\lambda }{3}$
   

Q.

A concave mirror is used for image formation for different positions of an object. What inferences can be drawn about the following when an object is placed at a distance of $10cm$from the pole of a concave mirror of a focal length of$15cm$?

(a) Position of the image($v$)

(b) Size of the image($m$)

(c) Nature of the image

Draw a labeled ray diagram to justify your inferences.

Q.

Define 1 dioptre of power of a lens.

Q.

Double-convex lenses are to be manufactured from a glass of refractive index 1.55, with both faces of the same radius of curvature. What is the radius of curvature required if the focal length is to be 20 cm?

Q. A convex lens is made up of three different materials as shown in the figure. For a point object placed on its axis, the number of images formed will be

1. 
   $1$
2. 
   $2$
3. 
   $3$
4. 
   $4$

Q.

A thin lens made of glass (refractive index $1.5$) of focal length $f=16cm$ is immersed in a liquid of refractive index $1.42$. If its focal length in liquid is $f_l$, then the ratio $\frac{f_l}{f}$ is closest to the integer.

1. $9$

2. $17$

3. $1$

4. $5$

Q. A thin glass (refractive index $1.5$) lens has optical power of $–5\text{D}$ in air. Its optical power in a liquid medium with refractive index $1.6$ will be

1. $-1\text{D}$
2. $25\text{D}$
3. $-25\text{D}$
4. $1\text{D}$

Q. Two concave mirrors each of radius of curvature $40cm$ are placed such that their principal axes are parallel to each other and at a distance of $1cm$ to each other. Both the mirrors are at a distance of $100cm$ to each other. Consider first reflection at $M_1$ and then at $M_2$. If the y-coordinate of the final image thus formed is found to be $-\frac{x}{5}\text{cm}$. Then find the value of $x$. (Take the location of the object as the origin).

Q.

(a) A giant refracting telescope at an observatory has an objective lens of focal length 15 m. If an eyepiece of focal length 1.0 cm is used, what is the angular magnification of the telescope?

(b) If this telescope is used to view the moon, what is the diameter of the image of the moon formed by the objective lens? The diameter of the moon is 3.48 × 10⁶ m, and the radius of lunar orbit is 3.8 × 10⁸ m.

Q.

The focal length of an equiconvex lens is equal to half the radius of curvature of either face. What is the refractive index of the material of the lens?

Q. Electromagnetic radiation of frequency $n$, wavelength $\lambda$, travelling with velocity $v$ in air, enters a glass slab of refractive index $\mu$. The frequency, wavelength and velocity of light in the glass slab will be respectively.

1. $\frac{n}{\mu },\frac{\lambda }{\mu },\frac{v}{\mu }$
2. $n,\frac{\lambda }{\mu },\frac{v}{\mu }$
3. $n,\lambda ,\frac{v}{\mu }$
4. $\frac{n}{\mu },\frac{\lambda }{\mu },v$

Q.

Why monochromatic light is used in Newton’s ring?

Q. An thin convex lens made from crown glass $(\mu =\frac{3}{2})$ has focal length $f$. When it is measured in two different liquids having refractive indices $\frac{4}{3}$ and $\frac{5}{3}$. It has the focal lengths $f_1$ and $f_2$ respectively. The correct relation between the focal length is:

1. $f_1=f_2<f$
2. $f_2>f$ and $f_1$ becomes negative
3. $f_1$ and $f_2$ both become negative
4. $f_1>f$ and $f_2$ become negative

Q. A double convex lens made of a material of refractive index 1.5 and having a focal length of 10 cm is immersed in liquid of refractive index 3.0. The lens will behave as

1. Converging lens of focal length 30 cm
2. Diverging lens of focal length 10 cm
3. Diverging lens of focal length $\frac{10}{3}cm$
4. Converging lens of focal length $\frac{10}{3}cm$

Q. 106.A spherical surface of radius of curvature R, separates air (refractive index 1.0) from glass (refractive index=1.5) the centre of curvature is in the glass A point object P placed in air is found to have a real image Q in the glass. the line PQ cuts the surface at a point O and PO=OQ.The distance PO is equal to:- 1)5R 2)3R 3)2R 4)1.5R

Q. Light guidance in an optical fibre can be understood by considering a structure comprising of thin solid glass cylinder of refractive index $n_1$ surrounded by a medium of lower refractive index $n_2$.
The light guidance in the structure takes place due to successive total internal reflections at the interface of the media $n_1$ and $n_2$ as shown in the figure. All rays with the angle of incidence $i$ less than a particular value $i_m$ are confined in the medium of refractive index $n_1$. The numerical aperture (NA) of the structure is defined as $\sin i_m$.

If two structures of same cross-sectional area, but different numerical apertures NA${}_1$ and $N{A}_2(N{A}_2<N{A}_1)$ are joined longitudinally, the numerical aperture of the combined structure is

1. $\frac{N{A}_{1}N{A}_2}{N{A}_1+N_2}$
2. $N{A}_1+N{A}_2$
3. $N{A}_1$
4. $N{A}_2$

Q. The power of a thin convex lens ${(}_a{\mu }_g=1.5)$ is +5.0 D. When it is placed in a liquid of refractive index ${}_a{\mu }_l$, then it behaves as a concave lens of local length 100 cm. The refractive index of the liquid ${}_a{\mu }_l$ will be

1. $\frac{5}{3}$
2. $\frac{4}{3}$
3. $\sqrt{3}$
4. $\frac{5}{4}$

Q. a parallel beam of monochromatic light ofwavelength 5000 A is inCident normally on a narrow slit of width of 0.001 mm. The light is focussed by Convex lens on a screen placed on focal plane.The central maxima is formed in the angular width of (1) 30^° (2) 60^° (3) 45^° (4)90^°

Q. An object is approaching a thin convex lens of focal length $0.3\text{m}$ with a speed of $0.01\text{m/s}$. The magnitude of the rate of change of position of image when the object is at a distance of $0.4\text{m}$ from the lens is

1. $0.09\text{m/sec}$
2. $0.01\text{m/sec}$
3. $0.04\text{m/sec}$
4. $0.02\text{m/sec}$

Q. A liquid in a capillary, rises up to a height $h$ when the capillary is vertical. If the capillary is inclined at angle ${45}^{\circ }$ with the vertical, then the length of liquid in capillary will be

1. $h$
2. $2h$
3. $\sqrt{2}h$
4. $\frac{h}{\sqrt{2}}$

Q.

Draw a labeled ray diagram to show the path of a ray of light incident obliquely on one face of a glass slab.

Q. Find the focal length of the lens shown in figure. The refractive index of lens material is $\frac{3}{2}$.

1. $-10\text{cm}$
2. $-20\text{cm}$
3. $+25\text{cm}$
4. $-30\text{cm}$

Q. A beam of parallel rays is brought to focus by a plano-convex lens. A thin biconcave lens of same focal length is joined to the first lens as shown in the figure. Which of the following statements is true?

1. The focus shifts to infinity.
2. The focal point shifts towards the first lens by a small distance.
3. The focal point shift away from the first lens by a small distance.
4. The focal point remains unchanged.

Q. A Galilean telescope has an objective lens of focal length $50\text{cm}$ and eyepiece of focal length $5\text{cm}$. If the telescope is used to focus an object $2\text{m}$ away from the objective lens, what should be the tube length? (Final image is forming at infinity.)

1. $66.67\text{cm}$
2. $45\text{cm}$
3. $61.67\text{cm}$
4. $71.67\text{cm}$