Focal length of a concave mirror and a convex lens अवतल दर्पण और उत्तल लेंस की फोकस दूरी
Aim: To find the approximate focal length of a concave mirror and of a convex lens by focusing a distant object on a screen, and to check it using several object distances (u–v method).
Apparatus उपकरण
- Concave mirror and convex lens with stands
- Screen (white cardboard) with stand
- Metre scale (least count 0.1 cm)
- A distant object such as a tree or building seen through a window
- Candle or illuminated object for the u–v method
Theory सिद्धांत
Rays from a very distant object are almost parallel. After reflection from a concave mirror or refraction through a convex lens they meet at the principal focus, so the distance from the mirror or lens to the sharp image is (approximately) the focal length f. For other object distances, use the mirror formula 1/v + 1/u = 1/f or the lens formula 1/v − 1/u = 1/f, with the New Cartesian sign convention (u is negative). For a concave mirror f is negative; for a convex lens f is positive.
Procedure विधि
- Distant object: place the mirror (or lens) facing an open window. Move the screen until a sharp, inverted, diminished image of a distant tree or building forms on it.
- Measure the distance between the mirror/lens and the screen. Repeat three times and take the mean.
- u–v method: place an illuminated object at a known distance u (more than f) from the mirror or lens.
- Move the screen to get the sharpest image and note the image distance v.
- Repeat for three or more values of u and calculate f each time using the formula.
Simulated experiment अनुकरण प्रयोग
Point the mirror at a tree far outside the window and slide the screen until the image is sharpest. Repeat three times.
Blurred: keep moving the screen.
Observation table: concave mirror प्रेक्षण तालिका
| S. No. | Distance of screen from mirror (cm) | Sharp? |
|---|---|---|
| Focus the image and record the distance. | ||
Mirror formula: 1/f = 1/v + 1/u, so f = uv/(u + v). For a concave mirror u, v and f are negative.
Take three readings of the sharp image distance.
Precautions सावधानियाँ
- The distant object should be really far away (at least 20–30 m).
- Keep the mirror or lens, the object and the screen at the same height and in a straight line.
- Find the sharpest image by moving the screen slowly back and forth.
- Measure distances from the pole of the mirror or the optical centre of the lens.
- Do not look at the Sun or focus sunlight on paper or skin.
Sources of error त्रुटि के स्रोत
- The distant object is not at infinity, so the measured distance is slightly more than f.
- Judging the sharpest position of the image is difficult; the image looks sharp over a small range.
- The stands may not be exactly upright, or distances may be measured from the base instead of the centre.
- Thick lenses and mirrors with large aperture give slightly blurred images (aberration).
Viva voce questions मौखिक प्रश्न
Q1. Why do we use a distant object to find the focal length quickly?
Rays from a distant object are almost parallel, and parallel rays meet at the focus after reflection or refraction, so the image forms at F.
Q2. What is the nature of the image of a distant object formed by a concave mirror?
Real, inverted and highly diminished, formed at the focus.
Q3. What is the relation between focal length and radius of curvature of a spherical mirror?
f = R/2.
Q4. Can you find the focal length of a convex mirror or concave lens by this method? Why?
No. They form virtual images that cannot be caught on a screen.
Q5. What is the power of a convex lens of focal length 20 cm?
P = 1/f = 1/0.20 m = +5 dioptre.