# Lens Maker's Formula

## Trending Questions

**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 10

^{8}m/sec, the focal length of the lens is

- 30 cm
- 20 cm
- 10 cm
- 15 cm

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

- 1003 cm
- 2003 cm
- 5003 cm
- 7003 cm

**Q.**Two coherent point sources S1 and S2 vibrating in phase emit light of wavelength λ. The separation between the sources is 2λ. Consider a line passing through S2 and perpendicular to the line S1S2. Find the position of nearest minima.

- D=λ2

- D=5λ12

- D=7λ12

- D=λ3

**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

2

3

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.

$9$

$17$

$1$

$5$

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

- −1 D
- 25 D
- −25 D
- 1 D

**Q.**Two concave mirrors each of radius of curvature 40 cm are placed such that their principal axes are parallel to each other and at a distance of 1 cm to each other. Both the mirrors are at a distance of 100 cm to each other. Consider first reflection at M1 and then at M2. If the y-coordinate of the final image thus formed is found to be −x5 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 × 10^{6}
m, and the radius of lunar orbit is 3.8 × 10^{8}
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 λ, travelling with velocity v in air, enters a glass slab of refractive index μ. The frequency, wavelength and velocity of light in the glass slab will be respectively.

- nμ, λμ, vμ
- n, λμ, vμ
- n, λ, vμ
- nμ, λμ, v

**Q.**

Why monochromatic light is used in Newton’s ring?

**Q.**An thin convex lens made from crown glass (μ=32) has focal length f. When it is measured in two different liquids having refractive indices 43 and 53. It has the focal lengths f1 and f2 respectively. The correct relation between the focal length is:

- f1=f2<f
- f2>f and f1 becomes negative
- f1 and f2 both become negative
- f1>f and f2 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

- Converging lens of focal length 30 cm
- Diverging lens of focal length 10 cm
- Diverging lens of focal length 103cm
- Converging lens of focal length 103cm

**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 n1 surrounded by a medium of lower refractive index n2.

The light guidance in the structure takes place due to successive total internal reflections at the interface of the media n1 and n2 as shown in the figure. All rays with the angle of incidence i less than a particular value im are confined in the medium of refractive index n1. The numerical aperture (NA) of the structure is defined as sinim.

If two structures of same cross-sectional area, but different numerical apertures NA1 and NA2(NA2<NA1) are joined longitudinally, the numerical aperture of the combined structure is

- NA1NA2NA1+N2
- NA1+NA2
- NA1
- NA2

**Q.**The power of a thin convex lens (aμg=1.5) is +5.0 D. When it is placed in a liquid of refractive index aμl, then it behaves as a concave lens of local length 100 cm. The refractive index of the liquid aμl will be

- 53
- 43
- √3
- 54

**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 m with a speed of 0.01 m/s. The magnitude of the rate of change of position of image when the object is at a distance of 0.4 m from the lens is

- 0.09 m/sec
- 0.01 m/sec
- 0.04 m/sec
- 0.02 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∘ with the vertical, then the length of liquid in capillary will be

- h
- 2h
- √2h
- h√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 32.

- −10 cm
- −20 cm
- +25 cm
- −30 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?

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

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

- 66.67 cm
- 45 cm
- 61.67 cm
- 71.67 cm