Table of Contents

## Aim/Aim of Experiment

To Find the Focal length of A Concave lens Using A Convex lens.

## Apparatus/Material Required

- An Optical bench with four Uprights
- A Convex lens (less focal length)
- A Concave lens (high focal length)
- Two Lens holders
- Two Optical needles
- A Knitting needle
- A half Meter scale.

## Theory

A concave lens always forms a virtual image, so its focal length cannot be found directly as like a convex lens. To find the focal length of a concave lens, indirect method is used.

**Indirect Method** – An object needle O is placed on one side of a convex lens L1 and its real inverted image I is located on the other side (by the image needle) as shown in the ray diagram.

The convex lens L2 is placed between the convex lens L1 and the image needle I. The concave lens diverges the rays and the image is now formed at I’ as shown in the ray diagram.

For concave lens, I is the virtual object and I’ is the real image. Hence, O2I=u & O2I’=v, as shown in the ray diagram.

So, focal length can be calculated by using the formula: 1/f=1/v-1/u.

From lens formula, we have, f=uv/u-v ,

where f = focal length of concave lens L2, u = distance of I from optical centre of L2, v = distance of I’ from optical centre of L2.

(Note:- According to sign convention, u and v have positive values (being measured in direction of incident light. since v>u, u-v is negative. Hence f comes negative).

## Ray Diagram

## Procedure

**To determine rough focal length of convex lens:**

- Mount the convex lens in lens holder.
- Go outside and point the lens at a distant tree or building.
- Get the image of the tree or building on a white colored wall (screen) and move the lens back and forth to get a sharp image on the wall.
- Now measure the distance between the lens and the wall (screen). it will equal rough focal length of the mirror.

**To set the convex lens:**

- Clamp the holder with the lens to a stable upright and place the upright at the 50 cm mark.
- Adjust the lens such that its surface is perpendicular to and perpendicular to the length of the optical bench.
- Keep the upright fixed throughout in this position.

**To set the object needle:**

- Take the thin optical needle as the object needle (O). Mount it vertically upwards on the outer side near the zero end nearly 1.5 times the rough focal length of the lens.
- Adjust the height of the object needle to make its tip on the horizontal line through the optical center of the lens.
- Note the position of the index mark vertically at the base of the object needle.

**To set the image needle:**

- Remove the convex mirror keeping it upright in its position.
- An inverted and enlarged image of the object needle will appear, tip of the image should be at the center of the lens.
- Place the thick optical needle (image needle) on the fourth end of the optical bench directly next to the other.
- Adjust the height of the image needle so that its tip appears in line with the tip of the image when viewed with the right open eye.
- Note the position of the index mark directly at the base of the image needle.

**To set the concave lens:**

- Clamp the holder with the concave lens perpendicular to the I side of the convex lens.
- Fix it upright at a distance from the convex lens.
- Set the convex lens surface with the principal axes of the lenses in the same direction as the convex lens surface.

**To set the image needle at I’:**

- Take the thin optical needle as object needle (O). Mount it in outer laterally move- able upright near zero end.
- Keep the upright fixed throughout in this position.

**To get more observations:**

- Move the object needle 2 cm towards lens and the two cm away from the lens.
- Repeat the experiment to get more observations.

## Observations

- Rough focal length of the convex lens = _ cm.
- Actual length of the knitting needle, x = _ cm.
- Observed distance between the concave lens and image needle when knitting needle is placed between them, y = _ cm.
- Index correction for u as well as v, (x-y) = _ cm.
- Observation Table for focal length of Concave lens:

Sr. No. | O (cm) | L1 at O1 (cm) | I (cm) | L2 at O2 (cm) | I’ (cm) | u=IO2 (cm) | v=I’O2 (cm) | u=IO2 (cm) | v=I’O2 (cm) | f=uv/u-v (cm) |
---|---|---|---|---|---|---|---|---|---|---|

(1) | (2a) | (2b) | (2c) | (2d) | (2e) | (3a) | (3b) | (4a) | (4b) | (5) |

1. | 34.5 | 50 | 86.8 | 72.5 | 91.2 | 14.3 | 18.7 | 14.3 | 13.8 | -28.52 |

2. | 32.9 | 50 | 91.4 | 78.7 | 94.8 | 12.7 | 16.1 | 11.7 | 11.2 | -23.4 |

3. | 32 | 50 | 95 | 82.8 | 98.7 | 12.2 | 15.9 | 11.8 | 11.3 | -23.21 |

- Mean value of focal length, (Mean f) = f1+f2+f3/3 =-75.13/3 = -25.04 cm.

## Calculations

- Find difference of positions of L2 and I and write it as observed u in column 3a.
- Find difference of positions of L2 and I’ and write it as observed v in column 3b.
- Apply index correction and write corrected values of u & v in columns 4a and 4b.
- Calculate f=uv/u-v and write in column 5.
- Take mean of different values of as recorded in column 5.

## Result

The focal length of given Concave lens using Convex Lens is, f = -25.04 cm.

## Precautions

- The Concave & Convex lenses must be neat & clean.
- To make the combination is convex, the focal length of the convex lens should be less than the focal length of concave lens.
- While removing the parallax, the eye should be kept at least 30 cm from the needle.
- Must be applied the index correction of u and v to get clear observations.

## Sources of Error

- The upright may not be vertical.
- Parallax removal may not be perfect.
- The focal length of convex lens may not be small.

## Viva Voice Questions with Answers

**1.** Define a spherical lens.

**Answer:** A piece of a transparent medium bounded by atleast one spherical surface, is called a spherical lens.

**2.** Describe different types of spherical lenses.

**Answer:** There are two types of spherical lenses:

**Convex or Converging Lenses:**These are thick in the middle and thin at the edges.**Concave or Diverging Lenses:**These are thin in the middle and thick at the edges.

**3.** Describe different types of convex lenses.

**Answer:** There are three types of convex lenses:

- Double convex.
- Plano-convex.
- Concavo-convex.

**4.** Describe different types of concave lenses.

**Answer:** There are three types of convcave lenses:

- Double concave.
- Plano-concave.
- Convexo-concave.

**5.** Mention three special rays of lens.

**Answer:** Three spacial rays of lens are:

- Incident on the lens parallel to principal axis. After refraction from the lens, it actually passes through second principal focus F2 (in case of a convex lens) or appears to come from the second principal focus F2 (in case of a concave lens).
- Incident on the lens through first principal focus F1 (in case of a convex lens) or in direction of first principal focus F1 (in case of a concave lens). After refraction from the lens, it goes parallel to the principal axis.
- Incident on the lens in direction of optical centre. It passes undedicated through the lens.

**6.** Define sign convention of lenses.

**Answer:** It is a convention, which fixes the sign of different distances measured. The sign convention followed is the New Cartesian sign convention.

**7.** Give rules of sign convention of lenses.

**Answer:** It gives following rules:

- All distances are measured from the optical centre of the lens (along the principal axis).
- The distances measured in the same direction as the direction of incident light, are taken as positive.
- The distances measured opposite to the direction of incident light, are taken as negative.
- The distances measured above the principal axis are taken as positive but distances measured below the principal axis are taken as negative.

**8.** Give facts obtained from sign convention of lenses:

**Answer:** According to above mentioned rules of sign convention:

- Focal length for a convex lens is taken positive and the same for concave lens is taken negative.
- The distance of an object is always negative.
- The distance for real image is positive, while that for a virtual image is negative.
- The size of object is positive and size of real image is negative while size of virtual image is positive.

**9.** Define and give lens formula.

**Answer:** The equation relating the object distance (u), the image distance (v) and the lens focal length (f), is called lens formula. It is also called Gaussian formula.

The Lens formula is, 1/v-1/u=1/f.

**10.** Describe various assumptions made in derivation of lens formula.

**Answer:** Following assumptions are made in derivation of the lens formula:

- The lens is thin.
- The lens has a small aperture.
- The point object lies on to the principal axis and placed perpendicular.
- The incident rays make small angles with the lens surface or the principal axis.

**11.** Define power of a lens. Give its unit and sign.

**Answer:** It is the capacity or ability of a lens to deviate (converge or diverge) the path of rays passing through it. A lens producing more converging or more diverging is said to have more power and vice-versa. It is represented by the symbol P.

A lens of less focal length produces more converging or diverging rays and is said to have more power. Hence, Power = 1/focal length or P~1/f,

we have P=1/f, (constant of proportionality is taken as 1).

**Unit:** Unit of power is diopter (D). One diopter is the power of a lens of focal length 1 metre.

**Sign:** A converging lens has positive focal length and positive power. A diverging lens has negative focal length and negative power.

**12.** Define a lens combination. Give expression for its focal length, power and magnification.

**Answer:** Definition: Two or more thin lenses, placed in contact together to have a common principal axis, form a lens combination.

**Focal length:** If f1, f2…., fn be the focal length of individual lens and F be the focal length of the combination then,

Expression for focal length of the combination of lenses, 1/f=1/f1+1/f2+1/f3…..1/fn.

**Power:** If P1, P2,….., Pn be the power of individual lenses and P be the power of the combination then,

Expression for power of the combination of lenses, P=P1+P2+P3…..Pn.

**Magnification:** If m1, m2,….., mn are the magnification of individual lenses and m is the equivalent magnification of the combination then,

Expression for magnification of the combination of lenses, m=m1×m2×m3…..×mn.

**13.** Define chromatic aberration.

**Answer:** The defect or drawback of a lens due to which it makes a coloured image of an object illuminated with white light, is called chromatic aberration. It is due to dispersion of white light by lens (just like a prism does).

**14.** What is Remedy.

**Answer:** It is removed by combining a convex and a concave lens of suitable focal length and material. The combination of two lenses is called an achromatic combination (a chromic doublet).

**15.** Which convex lens has more focal length, thick or thin?

**Answer:** A thin convex lens has more focal length.

**16.** Can you find rough focal length of a concave lens?

**Answer:** No, because it does not form a real image to be obtained on a screen.

**17.** What is the type of the eye lens?

**Answer:** The eye lens is convex.

**18.** What are the practical uses of lenses?

**Answer:** Lenses are used in spectacles, microscopes, telescopes and other optical instruments.

**19.** How can a convex lens be used as a magnifier?

**Answer:** For this purpose the lens is put very close to the eye in between the eye and the object to be magnified.

**20.** Define optical centre of a lens.

**Answer:** It is a fixed point inside the lens on its principal axis, through which fight rays passing undedicated.

**21.** What is the principal axis of a lens?

**Answer:** The straight fine passing through the centres of curvature of the curved surfaces of the lens is called the principal axis of the lens.

**22.** What is the principal focus of a lens?

**Answer:** It is fixed point on the principal axis of a lens where a beam of fight incident parallel to its principal axis converges or appears to diverge after passing through the convex lens or concave lens.

**23.** What is the focal length of a lens?

**Answer:** It is the distance between optical centre and principal focus of a lens. Its S.I. unit is metre.

**24.** Define S.I unit of power.

**Answer:** The Diopter is the S.I. unit of power. One diopter is the power of lens whose focal length is one metre.

**25.** What are the sign for the power of a convex lens and concave lens?

**Answer:** The power of a convex lens is positive since its focal length is positive while the power of a concave lens is negative since its focal lens is negative.

**26.** What is a lens maker formula?

**Answer:** It is relation between focal length, radii of curvature, refractive index of material of lens and refractive index of surroundings.

**27.** What are the factors affecting the power of lens?

**Answer:** Following factors affecting the power of lens:

- Refractive index of lens material.
- Refractive index of surroundings i.e., change of medium.
- Radii of curvature.
- Wavelength of light.
- Thickness of lens.

**28.** How the power of lens charge w.r.t. the two surrounding medium?

**Answer:** The power of a lens is maximum for vacuum or air and it decreases with increase in two refractive index of medium.

**29.** How the power of lens charge w.r.t. to wavelength of light?

**Answer:** The power of a lens is different for different colour of light. The power of a lens is maximum of violet and minimum for red colour light.

**30.** Does power depend upon aperture of a lens?

**Answer:** No. Power doesn’t depend upon aperture of a lens.

**31.** Under what condition, the nature of lens change?

**Answer:** The refractive index of surrounding medium is greater them that of material of lens. The convex lens act as concave lens and vice-versa.

**32.** Under what condition, a lens does not show the refraction.

**Answer:** When refractive index of surrounding medium is equal to refractive index of material of lens.

P=1/f = [(n2/n1)-1](1/R1-1/R2), Since n2=n1, P=0.

**33.** Why goggles (Sun glasses) have zero power?

**Answer:** The surfaces are curved in same direction and of same radius.

P = [(n2/n1)-1](1/R1-1/R2) = 0.

**34.** What type of lens is an air bubble inside water?

**Answer:** Concave lens.

**35.** Define refractive index.

**Answer:** It is the property of a transparent medium which resist the propagation of light in that medium. It is measured in term of speed of light in a medium w.r.t. speed of light in vacuum.

**36.** What is relative refractive index?

**Answer:** Relative refractive index of medium 2 w.r.t. medium 1 is the ratio of the speed of light in medium 1 to the speed of light in medium 2.

1n2=n2/n1=V1/v2, It doesn’t have any emit or dimensions.

**37.** What is absolute refractive index?

**Answer:** Absolute refractive index of a medium is the ratio of the speed of light in vacuum to the speed of light in that medium.

Refractive Index, n=R.I. of the medium/R.I. of the vacuum = c/v.

**38.** Is the absolute refractive can be less than unit?

**Answer:** No. The absolute refractive can’t be less than unit.

**39.** What is the power of combination of a convex and concave lens of the same focal length?

**Answer:** Zero.

**40.** Why is the rough focal length of concave lens not determine?

**Answer:** It makes virtual image for all positions of objects.

**41.** How chromatic aberration can be minimized?

**Answer:** It can be minimized by taking thin and small aperture lens.

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