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प्रश्न
A convex lens produces an inverted image magnified three times of an object placed at a distance of 15 cm from it. Calculate focal length of the lens.
उत्तर
Given:
Object distance, u =-15 cm
Magnification, m =-3 (Image is inverted.)
Applying magnification formula, we get:
m = v/u =-3
or, v/(-15) = -3
or, v = 45 cm
Applying lens formula, we get:
1/v - 1/u = 1/f
1/45- 1/(-15) = 1/f
1/f = ( 1+3 )/45
1/f = 4/45
or f = 11.2 cm
Hence, focal length of the lens is 11.2 cm.
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संबंधित प्रश्न
(a) Draw a ray diagram to show the formation of an image by a convex lens when an object is placed in front of the lens between its optical centre and principal focus.
(b) In the above ray diagram, mark the object distance (u) and the image distance (v) with their proper signs (+ve or –ve as per the new Cartesian sign convention) and state how these distances are related to the focal length (f) of the convex lens in this case.
(c) Find the power of a convex lens which forms a real and inverted image of magnification –1 of an object placed at a distance of 20 cm from its optical centre.
Analyse the following observation table showing variation of image-distance (v) with object-distance (u) in case of a convex lens and answer the questions that follow without doing any calculations :
| S. No. | Object-Distance u (cm) |
Image-Distance v (cm) |
| 1 | –100 | +25 |
| 2 | –60 | +30 |
| 3 | –40 | +40 |
| 4 | –30 | +60 |
| 5 | –25 | +100 |
| 6 | –15 | +120 |
(a) What is the focal length of the convex lens? Give reason to justify your answer.
(b) Write the serial number of the observation which is not correct. On what basis have you arrived at this conclusion?
(c) Select an appropriate scale and draw a ray diagram for the observation at S.No. 2. Also find the approximate value of magnification.
A beam of light travelling in air is incident of water. Draw a ray-diagram indicating the change in its path in water.
What type of lens is shown in the diagram on the right? What will happen to the parallel rays of light? Show by completing the ray diagram.
How could you find the focal length of a convex lens rapidly but approximately?
An object 4 cm high is placed at a distance of 10 cm from a convex lens of focal length 20 cm. Find the position, nature and size of the image.
What kind of lens can form:
an inverted magnified image?
Study the diagram below.
what are the points O, O’ called?
A pin 2 cm long is placed 12 cm away from a convex lens at right angles to the principal axis. If the focal length of the lens is 20 cm, by scale drawing find the size of the image and its magnification.
A convex lens forms an inverted image of size same as that of the object which is placed at a distance 60 cm in front of the lens. Find: The position of image
