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# Determination of Focal Lengths of Concave Mirror and Convex Lens

Last updated date: 02nd Aug 2024
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## Physics Experiment - An Introduction to Determination of Focal Lengths of Concave Mirror and Convex Lens

We all have used a magnifying glass at some point or the other to enlarge the object we are viewing. Why is it that at a particular point from the glass the object is magnified to the maximum? We have often seen in our homes Dish TVs and in the pictures of satellites the antennae has a curved surface with a large bulb at some distance from it. Likewise, there are many instances of starting a fire using a magnifying glass by converging the sun's rays at a point on the paper, keeping at a fixed distance. This special distance is known as the focal length.

In this simple experiment, we are going to learn how to determine the focal length of a concave mirror with sign and the focal length of convex lens with sign.

• Aim

• Theory

• Procedure

• Observations

• Result

### Aim

To determine the focal length of Concave mirror and Convex lens with sign.

### Apparatus Required

1. A concave mirror

2. A convex lens

3. A white cardboard

4. One mirror holder

5. One lens holder

6. One image holder

7. A measuring scale

### Theory

The Focal length (f) of curved mirrors and lenses is the distance from their optical centers to a point where the light rays meet after reflection/ refraction. The focal length of an optical device determines the capacity of the device to reflect (for mirrors) or refract (for lenses) the light rays and is equal to half the radius of curvature.

In a concave mirror, a real and inverted image is formed of the reflected light rays from the object on the same side of it. In a convex lens, the image is formed using a similar mechanism and the reflected light rays are refracted through the lens. The image is formed on the other side of the object.

Image formation by a concave mirror

Image formation by a convex mirror

In this experiment, we are going to determine the focal lengths (f) of both the devices using the above concept by obtaining the real and inverted image of a far object on a screen.

### Procedure

1. Clean the surfaces of the mirror and lens using a solution of vinegar and water in the ratio 1:4.

2. Note down the least count of the meter scale.

3. First clamp the full length of mirror with a stand on the mirror holder and keep its reflecting surface towards one of the windows  (see Image 3 for reference).

4. Clamp the white cardboard on the image holder and place it on the scale between the mirror and the window (see Image 3 for reference).

5. By adjusting the positions of the mirror and the cardboard on the scale, try to obtain the image of an object from the outside of the window (such as a tree) on the cardboard. The image will be inverted in nature (see Image 3 for reference).

6. Adjust both positions till you get the sharpest image.

7. Note down the distances of both the sliders using meter scale (see Image 3 for reference).

8. Repeat the step two more times. Note the observations of the distances in a table.

9. Now remove the mirror with its holder and clamp the convex lens on its holder (see Image 4 for reference).

10. Place the lens with its holder on the scale between the window and the cardboard (see Image 4 for reference).

11. Try to obtain the same image on the screen by varying both the holders. Note the positions corresponding to the sharpest images so obtained (see Image 4 for reference).

12. Repeat the procedure two more times. Note the readings in a separate table.

Experimental setup for the determination of the focal length of a concave mirror.

Experimental setup for the determination of the focal length of a thin convex lens.

### Observations

We'll be tabulating the various positions of the device and the screen. The focal length is given by the distance between the device and the screen in each case.

### Observation Table

 Sr-No Position Of Mirror|M| (cm) Position Of Screen|v| (cm) Focal Length   \[f = |M - v|\] (cm) 1 2 3

### (i) Convex lens

 Sr-No Position Of Lens |L| (cm) Position Of Screen|v| (cm) Focal Length\[f= |v - L| (cm)\] 1 2 3

### Result

Average focal length of concave mirror \[ = ............\;cm\]

Average focal length of convex lens \[= …………\;cm\]

### Precautions

1. The rays of light should be directly incident from the far object on the optical devices without any obstacle in between.

2. All the holders and stands should be straight and parallel.

3. Optical devices and screens should be in the same straight line in each case.

4. The surfaces of devices should be properly cleaned.

5. Positions should be noted only after obtaining the sharpest image on the screen.

## Lab Manual Questions

1. How will you distinguish between a convex and concave lens?

Ans: A convex lens is the one which is thicker at the middle and thinner at the edges. When placed in front of a distant light source, a convex lens converges all the light from the source to one single point on a side away from the source. On the other hand, a concave lens is the one which is thinner at the middle and thicker at the edges. When placed in front of a distant light source, a convex lens diverges all the light from the source uniformly in all directions on a side away from the source.

1. Can this method be used to find the approximate focal length of a concave lens?

Ans: No, this method cannot be used to find the approximate focal length of a concave lens. This is because a concave lens does not form a real image of an object placed at infinity. So, the observer is incapable of producing the image on a screen and hence measures its distance.

1. What type of mirror is used in a torch? Give reasons.

Ans: A concave mirror is used in the torch. This is because when a glowing bulb is placed at the focus of a concave mirror, its light is reflected from the mirror as a parallel beam.

1. What type of mirror is used as a shaving mirror? Why?

Ans: A concave mirror is used as a shaving mirror. This is because when an object is placed very close to such a mirror, a virtual and magnified image of the object is observed.

## Viva Questions

1. Why don't full length mirrors have a radius of curvature?

Ans: Full length mirrors are plain mirrors which are not a part of a sphere. Hence, they have no associated radius of curvature and are said to be infinite. Likewise, they have no associated characteristics as that of curved mirrors/ lenses such as principal axis, principal focus and optical center.

1. How are spherical mirrors different from plain mirrors?

Ans: Spherical mirrors are made up of curved surfaces and have associated center of curvature, focus, optical center and principal axis, enabling them to form a real image of the object. Plain mirrors do not have such characteristics.

1. Define the center of curvature of an optical device.

Ans: The center of curvature of an optical device is the center of the sphere of which the device is carved out as an arc. This is a point lying on the principal axis and is twice as far from the principal focal from the optical center of the device.

1. Which optical devices form virtual and erect images?

Ans: Convex mirror and concave lens produce virtual and erect images as the light rays reflected from the object do not actually meet at any given point, but only apparently meet to the observer. Such images cannot be obtained on the screen.

1. In which case the image formed by a concave mirror is virtual and erect?

Ans: When the object is placed between principal focus and pole, the image formed is virtual and erect and the light rays reflected from the object do not actually meet at any point.

1. How does the size of the image formed by a convex lens change as the object approaches the lens?

Ans: As the object approaches the lens, the size of the image so formed increases. This image is real and inverted in nature and forms on the other side of the lens. Hence, the magnification also increases. This finds a practical application in the magnifying glasses.

1. What is the working principle of optical mirrors?

Ans: Optical mirrors are based on the principle of reflection of light. When the light rays strike the object and get reflected, they are incident towards the mirror surface and follow laws of reflection. Hence, the light waves get reflected again and meet to form the image of the object.

1. What is the working principle of optical lenses?

Ans: Optical lenses are based on the principle of refraction of light. When the light rays strike the object and get reflected, they are incident towards the lens surface and follow Snell’s laws of refraction. Hence, the light waves get refracted and meet to form the image of the object.

1. How does the mirror formula differ from lens formula?

Ans: In mirror formula, the reciprocal of focal length is given by the sum of the individual reciprocals of the image distance and object distance. In the lens formula, the reciprocal of focal length is given by the difference of the individual reciprocals of the image distance and object distance.

1. Do lenses refract light of all frequencies?

Ans: Yes, optical lenses are capable of refracting lights of all frequencies of the electromagnetic spectrum.

## Practical Based Questions

1. Optical lenses are based on:

1. Reflection

2. Interference

3. Refraction

4. Polarization

Ans: (C)

1. Which of the following always produces a virtual image?

1. Convex mirror

2. Concave mirror

3. Convex lens

4. None of the above

Ans: (A)

1. Which of the following is thicker at the middle but thinner at the ends?

1. Concave mirror

2. Convex mirror

3. Concave lens

4. Convex lens

Ans: (D)

1. For radius of curvature R and focal length f, which of the following relations is correct?

1. R = 4f

2. R = 2f

3. R = f

4. R = 3f

Ans: (B)

1. Which mirror is commonly used in our homes?

1. Full length mirror with stand

2. Concave mirror

3. Convex mirror

4. Inclined mirror

Ans: (A)

1. Which substance has the highest reflectivity?

2. Silver

3. Mercury

4. Bismuth

Ans: (B)

1. Pick the field in which spherical mirrors do not find applications.

2. Rear view mirrors

4. Security mirrors

Ans: (C)

1. Which of the following is capable of igniting a fire using sun rays?

1. Concave mirror

2. Convex mirror

3. Concave lens

4. Convex lens

Ans: (D)

1. What is the focal length of a full length mirror with a stand?

1. 1 meter

2. 100 meters

3. 1000 meters

4. Infinity

Ans: (D)

1.  What is the sign of image distance in a convex lens?

1. Positive

2. Negative

3. Depends on object size

4. Depends on image size

Ans: (A)

## Conclusion

From the above experiment, we can conclude that the concave mirror and convex lens produce the real and inverted image of an object. Curved mirrors are carved out of a glassy sphere and hence have certain spherical parameters, while plain mirrors do not have such.

We also learnt various concepts related to such mirrors and lenses and a practical way to determine the focal lengths of the same.

We hope to enlighten the reader about various concepts of the topic, serving as a motivation to further explore the opportunities in the field for time to come.

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