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प्रश्न
Define power of a lens. Write its units. Deduce the relation `1/f =1/f_1 +1/f_2`for two thin lenses kept in contact coaxially.
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उत्तर
Consider two lenses A and B of focal length f1 and f2 placed in contact with each other. An object is placed at a point O beyond the focus of the first lens A. The first lens produces an image at I1 (real image), which serves as a virtual object for the second lens B, producing the final image at I.
Since the lenses are thin, we assume the optical centers (P) of the lenses to be co-incident. For the image formed by the first lens A, we obtain
`1/v_1 -1/u =1/f_1 ........ (1)`
For the image formed by the second lens B, we obtain
`1/v -1/v_1 =1/f_2 ........ (2)`
Adding equations (1) and (2), we obtain
`1/v -1/u =1/f_1 + 1/f_2 ........ (3)`
If the two lens system is regarded as equivalent to a single lens of focal length f, we have
`1/v -1/u =1/f_1 ........ (4)`
From equations (3) and (4), we obtain
`1/f_1 + 1/f_2 =1/f_1 `
संबंधित प्रश्न
You have two lenses A and B of focal lengths +10 cm and –10 cm, respectively. State the nature and power of each lens. Which of the two lenses will form a virtual and magnified image of an object placed 8 cm from the lens? Draw a ray diagram to justify your answer
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Fill in the following blank with suitable word:
For converging lenses, the power is __________ while for diverging lenses, the power is ___________.
An object of height 4 cm is placed at a distance of 15 cm in front of a concave lens of power, −10 dioptres. Find the size of the image.
The power of a combination of two lenses X and Y is 5 D. If the focal length of lens X be 15 cm :
(a) calculate the focal length of lens Y.
(b) state the nature of lens Y.
State the condition for the following a ray passes undeviated through the lens .
If the lens is of focal length 25 cm. Calculate the power of the lens.
If there is a convex lens of focal length 75 cm and a concave lens of focal length 40 cm, then calculate their combined power and combined focal length.
Match the following:
| Column - I | Column - II | ||
| 1 | Retina | a | Path way of light |
| 2 | Pupil | b | Far point comes closer |
| 3 | Ciliary muscles | c | near point moves away |
| 4 | Myopia | d | Screen of the eye |
| 5 | Hypermetropia | e | Power of accommodation |
When monochromatic red light is used instead of blue light in a convex lens, its focal length will ______.
