You are provided with a converging lens and holder, a screen, a ray box containing an illuminated object pin, and a meter rule. i. Place the lens in its hol...

You are provided with a converging lens and holder, a screen, a ray box containing an illuminated object pin, and a meter rule.

i. Place the lens in its holder such that it is facing a distant object seen through a well-lit laboratory window. Move the screen to and fro until a sharp image of the distant object is formed on it. Measure the distance, \(f_{0}\), between the screen and the lens.

ii. Clamp the meter rule securely to the table. Place the illuminated object pin at the end R of the meter rule.

iii. Place the lens at a position P such that \(X = RP =\) 20cm.

iv. Move the screen to a position Q to receive a sharp image of the object. Measure the distance \(Y = PQ\).

v. Evaluate \(Z = (X+Y)\)

vi. Repeat the procedure for five other values of x = 25cm. 3Ocm, 35cm, 40cm and 45cm. In each case, record X,Y and evaluate Z.

vii. Tabulate the results.

viii. Plot a graph with Z on the vertical axis and X on the horizontal axis. Draw a smooth curve through the points.

ix. Determine from your graph the minimum value of \(Z=Z_{0}\) and its corresponding distance

x. Evaluate \(W = ½ \left(\frac{Z_0}{4} + \frac{X_0}{2}\right)\)

xi. State two precautions taken to ensure accurate results.

(b) i. Draw a ray diagram to show how a Convex lens forms an image of magnification less than one.

ii. Name two pairs of features in the human eye and a lens camera that performs similar functions.

(a) Determination of the focal length of a converging lens

On focusing the distant object sharply on the screen, the focal length obtained was:

\(f_0 = 13.0\text{ cm}\).

The readings obtained with the illuminated object pin were as follows.

S/N	\(X=RP\) (cm)	\(Y=PQ\) (cm)	\(Z=X+Y\) (cm)
1	20	60	80
2	25	38	63
3	30	30	60
4	35	26	61
5	40	24	64
6	45	21	66

Graph of \(Z\) against \(X\):

From the lowest point of the curve,

\(Z_0=60\text{ cm}\), and \(X_0=30\text{ cm}\).

\[W=\frac{1}{2}\left(\frac{Z_0}{4}+\frac{X_0}{2}\right)=\frac{1}{2}\left(\frac{60}{4}+\frac{30}{2}\right)=\frac{1}{2}(15+15)=15\text{ cm}.\]

Precautions

1. The object pin, optical centre of the lens and centre of the screen were kept at the same height and on one straight line.
2. The screen was moved until the image was sharply focused, and metre-rule readings were taken with the eye vertically above the mark to avoid parallax.

(b)(i) Ray diagram for a diminished image formed by a convex lens

The object is placed beyond \(2F_1\). The image formed is real, inverted and diminished, between \(F_2\) and \(2F_2\).

(b)(ii) Corresponding parts of the human eye and lens camera

Human eye	Lens camera
Retina	Film or image sensor
Eye lens	Camera lens
Iris	Diaphragm

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