Question

Determination of the focal length of a convex lens by \(u-v\) method. (Optional)

Set up a lamp, an object card (with a slit cut on it) and a white-paper screen on the table and place a metre scale by their side as shown in Fig. 9(b). Adjust the position of the lens so that a blurred image of the slit is obtained on the screen. An image on the screen may not be obtained if the slit is very near the lens. Having obtained a blurred image, move the screen back and forth till the image is sharply focussed on the screen. The slit and the lens must not be moved during this setting.

From the metre scale, measure the distance between the slit and the lens. This is the object distance \((u)\). Also measure the distance between the paper screen and the lens. This is the image distance \((v)\). Putting the values in the equation \[\frac{1}{v}+\frac{1}{u}=\frac{1}{f}\], the focal length \(f\) of the lens can be found out. The observations are to be repeated for different values of \(u\) and the mean value of \(f\) is to be found out.

Answer 1

This activity demonstrates how to determine the focal length ($f$) of a convex lens using the $u-v$ method. Below is the step-by-step logical deduction and observation procedure based on the provided text:

Aim: To find the focal length of a given convex lens using the relation between object distance ($u$) and image distance ($v$).

Apparatus Required:

• Convex lens
• Lamp (source of light)
• Object card (with a slit)
• White paper screen
• Metre scale
• Optical bench (implied by the setup on a table)

Theory/Formula:

The lens formula is used to calculate the focal length. The magnitude of the focal length ($f$) is determined by:

\[ \frac{1}{v} + \frac{1}{u} = \frac{1}{f} \]

Where:

• $u$ = Object distance (distance from the slit to the lens)
• $v$ = Image distance (distance from the screen to the lens)

Procedure:

1. Arrangement: Place the lamp, object card (slit), convex lens, and white screen on the table. Align them such that their centers lie on the same straight line (principal axis).
2. Measurement: Place a metre scale along the arrangement to measure distances accurately.
3. Obtaining Image: Adjust the position of the lens and screen. Ensure the object (slit) is not too close to the lens (closer than the focal point), as no real image will form on the screen in that case.
4. Focusing: Initially, you may get a blurred image. Keep the slit and the lens stationary. Move the screen back and forth until a sharp, focused image of the slit is obtained on the screen.
5. Recording Data:
   • Measure the distance between the slit and the lens. This is $u$.
   • Measure the distance between the screen and the lens. This is $v$.
6. Calculation: Substitute the values of $u$ and $v$ into the formula to calculate $f$.
7. Repetition: Repeat the procedure for at least three to five different values of $u$ (by moving the object and lens positions). Calculate $f$ for each trial.
8. Mean: Calculate the mean (average) value of the focal length obtained.

Observation Table Format:

S. No.	Object Position	Lens Position	Screen Position	Object Distance ($u$) [cm]	Image Distance ($v$) [cm]	Focal Length ($f$) [cm]
1
2
3

Calculation for each trial: \[f = \frac{uv}{u+v} \]

Mean Focal Length: \[ \bar{f} = \frac{f_1 + f_2 + f_3 + \dots}{N}\]

Precautions:

1. The center of the lens, the slit, and the screen must lie at the same height (on the principal axis).
2. The image must be sharply focused before taking readings.
3. Do not move the lens or the object while adjusting the screen for focus.
4. Readings should be taken without any parallax error.

Conclusion:

The focal length of the given convex lens is found to be \[ \bar{f}\] cm (value from calculation).