TEST OF PRACTICAL KNOWLEDGE QUESTION
You have been provided with a ray box, a converging lens, a lens holder, a screen, a metre rule, and half- metre rule. Use the diagram above as a guide to perform the experiment.
(i) Determine the approximate focal length f, of the lens by focusing a distant object on the screen.
(ii) Place the ray box and the screen such that the distance between the illuminated cross-Wire and the screen, \(D= 150\ \text{cm}\).
(iii) Place the lens at a position L where a sharp mage of the cross-Wire Is obtained on the screen Note L.
(iv) Move the lens at a position L, to 0btain another sharp image of the cross-wire on the screen. Note L
(V) Measure the distance, d. between \(L_1\) and \(L_2\).
(Vi) Evaluate \(D^2\): \(d^2\) and \(D^2 - d^2\).
(vii) Repeat the procedure for four other values of \(D = 130\text{cm}, 100\text{ cm}, 90\text{ cm}\) and \(80\text{ cm}\). in each case.evaluate \(D^2\); \(d^2\) and \(D^2 - d^2\).
(viii) Tabulate the result
(ix) Plot a graph with \(D^2 - d^2\) on the vertical axis and \(D\) on the horizontal axis.
(x) Determine the r values of D axis and Determine the slopes, S, of the graph.
(xi) Evaluate \(k = \frac{s}{4}\)
(xii) State two precautions taken to ensure accurate results.
(bi) Distinguish between a virtual image and. plain image?
(ii) With the aid of a ray diagram, explain how a converging lens produces a Virtual image
Principle (displacement method). With the object (illuminated cross-wire) and screen a fixed distance D apart, there are two positions of the converging lens, \(L_1\) and \(L_2\), that both give a sharp image on the screen. Let their separation be \(d = L_1 - L_2\). The focal length is
\[ f = \frac{D^{2}-d^{2}}{4D} \quad\Rightarrow\quad D^{2}-d^{2} = 4f\,D \]
Expected graph. A plot of \((D^{2}-d^{2})\) on the vertical axis against D on the horizontal axis is a straight line through the origin with slope
\[ s = 4f \]
Evaluating k.
\[ k = \frac{s}{4} = f \]
so k is numerically the focal length of the lens (and should agree with the rough focal length found by focusing a distant object).
Sample table (headings).
| D (cm) | \(D^{2}\) | \(L_1\) | \(L_2\) | \(d=L_1-L_2\) | \(d^{2}\) | \(D^{2}-d^{2}\) |
|---|
| 150 | - | - | - | - | - | - |
| 130 | - | - | - | - | - | - |
| 100 | - | - | - | - | - | - |
| 90 | - | - | - | - | - | - |
| 80 | - | - | - | - | - | - |
Two precautions.
- The image was focused as sharply as possible and the eye placed to avoid parallax when reading lens positions.
- The cross-wire, lens and screen were kept centred with their centres in a straight horizontal line throughout.
(b)(i) Real image versus virtual image. A real image is formed by the actual meeting of refracted rays, can be caught on a screen and is inverted; a virtual image is formed where the rays only appear to come from, cannot be caught on a screen and is upright.
(b)(ii) Virtual image with a converging lens. Place the object between the lens and its principal focus (\(u < f\)). A ray parallel to the axis refracts through the far focus; a ray through the optical centre goes straight on. The emergent rays diverge and, produced backwards, meet on the same side as the object to give a virtual, erect, magnified image.
Principle (displacement method). With the object (illuminated cross-wire) and screen a fixed distance D apart, there are two positions of the converging lens, \(L_1\) and \(L_2\), that both give a sharp image on the screen. Let their separation be \(d = L_1 - L_2\). The focal length is
\[ f = \frac{D^{2}-d^{2}}{4D} \quad\Rightarrow\quad D^{2}-d^{2} = 4f\,D \]
Expected graph. A plot of \((D^{2}-d^{2})\) on the vertical axis against D on the horizontal axis is a straight line through the origin with slope
\[ s = 4f \]
Evaluating k.
\[ k = \frac{s}{4} = f \]
so k is numerically the focal length of the lens (and should agree with the rough focal length found by focusing a distant object).
Sample table (headings).
| D (cm) | \(D^{2}\) | \(L_1\) | \(L_2\) | \(d=L_1-L_2\) | \(d^{2}\) | \(D^{2}-d^{2}\) |
|---|
| 150 | - | - | - | - | - | - |
| 130 | - | - | - | - | - | - |
| 100 | - | - | - | - | - | - |
| 90 | - | - | - | - | - | - |
| 80 | - | - | - | - | - | - |
Two precautions.
- The image was focused as sharply as possible and the eye placed to avoid parallax when reading lens positions.
- The cross-wire, lens and screen were kept centred with their centres in a straight horizontal line throughout.
(b)(i) Real image versus virtual image. A real image is formed by the actual meeting of refracted rays, can be caught on a screen and is inverted; a virtual image is formed where the rays only appear to come from, cannot be caught on a screen and is upright.
(b)(ii) Virtual image with a converging lens. Place the object between the lens and its principal focus (\(u < f\)). A ray parallel to the axis refracts through the far focus; a ray through the optical centre goes straight on. The emergent rays diverge and, produced backwards, meet on the same side as the object to give a virtual, erect, magnified image.
