Question

Readings of the experiment to find the focal length of a convex lens by plotting graphs between u and v or between 1/u and 1/v

Answer 1

We know, lens maker formula,

1 / V-1 / You = 1 / F

Where is the distance between the poles of the length, we have the distance of the object from the pole of the lens and f is the length of the focus.

The reason given is that the lens is a convex lens

Therefore, the focal length should be positive.

If we consider 1 / v = y, 1 / u = mx and 1 / f = c

So, graph 1 / v v / s is 1 / u y = mx + c [straight line] The graph is shown in the figure.

But when we want to plot graph VV / S,

Then the graph will be transitional. The graph is shown in another picture.

Answer 2

Explanation:

Calculation of the focal length by the graphical method:

1) u-v Graph

Choose a suitable but the same scale to denote v along the Y-axis and u along X-axis. As per sign conventions, v is positive, and u is negative. Plot the points for different rates of v and u from the observation table in the second section. The graph is a rectangular hyperbola, as represented in the graph between u and v.

Draw a line OA creating an angle of 45° with either axis bisecting ∠YOX’ and reaching the curve at point A. Draw AC and AB perpendicular on the Y and X’-axis, respectively. The values of v and u are the same for point A. The coordinates of point A should be (2f, 2f), as for a convex lens, when v=2f, u=2f.

Therefore, AB = AC = 2f or OB=OC = 2f

This implies that f = OB/2 and f = OC/2

Mean value of f = 15.052cm

2) Choose an apt but the same scale to denote 1/u along the X’-axis and 1/v along the Y-axis. As per sign conventions, 1/u is negative, and 1/v is positive. Plot the points for varied sets of values of 1/u and 1/v from the observation table. The graph evolves to be a straight line as represented in the graph between 1/v and 1/u.

The straight-line slices the two-axis OY and OX’ at an angle of 45° at points Q and P, respectively, creating equal intercepts on the axis. Calculate the distance between OQ and OP.

Then the focal length, f = 1/OP = 1/ OQ

= 0.479 cm

Explanation

ExplanationAnother u-v Graph (same as a concave mirror)

ExplanationAnother u-v Graph (same as a concave mirror)Choose an apt but the same scale to denote v along the Y-axis and u along the X’-axis. Note the points at distances v1, v2, v3,……. etc., along the OY-axis for various sets of observations from the resulting table.

ExplanationAnother u-v Graph (same as a concave mirror)Choose an apt but the same scale to denote v along the Y-axis and u along the X’-axis. Note the points at distances v1, v2, v3,……. etc., along the OY-axis for various sets of observations from the resulting table.Create straight lines connecting u3 with u1 with v1, u2 with v2, u3 with v3,………. etc. The lines meet at the intersection point K, as represented in the graph below.

ExplanationAnother u-v Graph (same as a concave mirror)Choose an apt but the same scale to denote v along the Y-axis and u along the X’-axis. Note the points at distances v1, v2, v3,……. etc., along the OY-axis for various sets of observations from the resulting table.Create straight lines connecting u3 with u1 with v1, u2 with v2, u3 with v3,………. etc. The lines meet at the intersection point K, as represented in the graph below.Draw KM and KL perpendicular on the Y-axis and X’-axis, respectively.

F = OL = OM

F = OL = OM= 1/0.479cm.