To Find v Value For Different u Values Of Concave Mirror Find Focal Length

Introduction

Concave mirrors are spherical mirrors whose reflecting surface is bent inward. The image formed by a concave mirror is either magnified, the same size, or even diminished. This image formation depends upon the position of the concave mirror with respect to focus, curvature, and pole.

Focal length is the measure of the convergence or divergence of light; in other words, it is the distance from the centre of the lens to the point at which the image of an object is formed. The focal length of a concave mirror depends upon the value of u and v. If the focal length is positive it converges to light and if the focal length is negative it diverges light.

Aim

To find v value for different u values of a concave mirror.

List of Materials To Be Required

• A concave mirror
• A mirror holder
• Two optical needles
• A measuring scale (half metre)
• An optical bench with three uprights
• A knitting needle

Principle

In a concave mirror with a focal length f, the image of an object placed at a distance u from the pole is formed at a distance v from the pole. The relation between u, v, and f is given by

Or

According to the sign conventions, In a concave mirror, u, v, and f all have negative values in a concave mirror.

Procedure of The Experiment

Finding Rough Focal Length

1. Place the concave mirror in the mirror holder. Face the mirror towards a tree or a distant building.
2. Now focus the mirror by moving it front and back, so that a sharp image of the object is obtained on a plane wall or a blank sheet of paper.
3. Now obtain the rough focal length by calculating the distance between the mirror and the image formed.

Mirror and Pin Set-Up

1. Mount the concave mirror vertically on one end of the optical bench. Adjust the object pin P₁ so that the image is formed. This will align the principal axis of the mirror parallel to the optical bench.
2. Place another pin P₂ in front of the reflecting surface of the pin. Now, adjust both P₁ and P₂ pins so that their heights become equal to the height of the mirror Pole P.

Index Correction

1. Place a thin straight index needle so that one end (A₁) touches the tip of the pin and the other end (B₁) touches the pole of the mirror. The difference between the distance between the tip of the pin and the pole gives the observed distance. The actual length of the needle is the actual distance between the point which is measured by the measuring scale.
2. Now, the difference between the actual and observed length gives a correction to be made.
3. Find the index correction for both P₁ and P₂ pins.

Object and Image Needle Set-Up

1. Place P₁ at almost 2F distance away from the mirror. Obtain an inverted image of the same size as the pin.
2. Now place P₂ on a bench, and adjust its height the same as P₁. Place a piece of paper on one tip and consider it as the object pin.
3. Now place the object pin at a distance between F and 2F.
4. Locate the image of the pin using another pin. Remove the parallax error between the image and the pin.
5. Note values of u (distance of the object) and v (distance of the image) from the mirror.
6. Repeat this experiment for different positions of the object and determine the value of v.
7. Lastly, after index correction, record the corrected values of u and v and determine the focal length.

Observation

1. The rough focal length of the concave mirror = … cm
2. The actual distance of the object from the concave mirror using index needle,
3. Observed distance of the object from the concave mirror = position of the concave mirror – position of object pin,
4. Index correction (e) = actual distance – observed distance

Similarly the index correction

Tabulation

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