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### To Find The Value Of V For Different Values Of U In Case Of A Concave Mirror And To Find The Focal Length

To find the value of v for different values of u in case of a concave mirror and to find the focal length.

Following are the materials required for this experiment:

We use mirror formula for the determination of focal length.

From the above equation, we get the focal length as:

The value of f will be negative. This is according to the sign-convention, u and v have negative values.

To determine the rough focal length

The rough focal length of the given concave mirror = …….

The actual length of the knitting needle, x = ……

Observed distance between the mirror and object needle when knitting needle is placed in between them, y = …….

Observed distance between the mirror and image needle when knitting needle is placed in between the, z = ……..

Index correction for the object distance, u = x – y = ±…….

Index correction for the image distance, v = x -z = ±…….

Table for u, v, (frac{1}{u}), and (frac{1}{v})

Calculations of the focal length by graphical method

u – v graph is obtained by considering u on the x’- axis and v on y’ – axis. According to sign conventions, u and v are negative. Using the observation table, plot different points for different values of u and v. The graph obtained will be a rectangular parabola.

On either axis draw a line OA making 45° and meeting at a point A. Draw AB and AD perpendicular on x’ and y’- axis. For point A, the values of u and v will be the same. The coordinates at A is (2f, 2f) as u and v are same for a concave mirror when the object is placed at the centre of curvature. Hence, u = v = R = 2f.

Hence the focal length of the concave mirror is obtained from the coordinates of A.

The focal length of the given concave mirror is determined from the following:

Ans: Lens formula is defined as the equation which explains the relation between object distance (u), image distance (v), and focal length of the lens (f).

Q2. What is the optical centre of a lens?

Ans: Optical centre of a lens is defined as the fixed point inside the lens on the principal axis through which light ray passes.

Q3. What is the principal axis of a lens?

Ans: Principal axis of a lens is the straight line passing through the centre of curvature of the lens.