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प्रश्न
A lens of focal length 12 cm forms an erect image three times the size of the object. The distance between the object and image is ______.
विकल्प
8 cm
16 cm
24 cm
36 cm
उत्तर
A lens of focal length 12 cm forms an erect image three times the size of the object. The distance between the object and image is 16 cm.
Explanation:
Given:
Magnification, M = 3
Focal length f = 12 cm
Image distance v = ?
Object distance u = ?
We know that:
`M = v/u`
Therefore
`3 = v/u`
3u = v
Putting these values in the lens formula, we get:
`1/v-1/u = 1/f`
⇒ `1/(3u)-1/u = 1/12`
⇒ `(1-3)/(3u) = 1/12`
⇒ `(-2)/(3u) = 1/12`
⇒`3u = −24`
⇒ `u = (-24)/3`
⇒ u = −8 cm
v = 3u = −8 × 3 = −24 cm
The distance between the object and image is
∣v − u∣ = ∣−24 − (−8)∣ = ∣−24 + 8∣ = ∣−16∣ = 16cm.
The distance between the object and image is 16 cm.
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संबंधित प्रश्न
A student has obtained an image of a well-illuminated distant object on a screen to determine the focal length, F1of the given spherical mirror. The teacher then gave him another mirror of focal length, F2 and asked him to obtain a focused image of the same object on the same screen. The student found that in order to focus the same object using the second mirror, he has to move the mirror away from the screen. From this observation, it may be concluded that both the spherical mirrors given to the student were (select the correct option)
(A) Concave and F1 < F2
(B) Concave and F1 > F2
(C) Convex and F1 < F2
(D) Convex and F1 > F2
Which one of these circumstances enables a concave mirror to be used as a shaving mirror?
Fill in the following blank with suitable word:
If the magnification has a plus sign, than image is ......... and.........
Magnification produced by a concave lens is always:
(a) more than 1
(b) equal to 1
(c) less than 1
(d) more than 1 or less than 1
If a magnification of, –1 (minus 1) is obtained by using a converging lens, then the object has to be placed:
(a) within f
(b) at 2f
(c) beyond 2f
(d) at infinity
An object is 0.09 m from a magnifying lens and the image is formed 36 cm from the lens. The magnification produced is:
(a) 0.4
(b) 1.4
(c) 4.0
(d) 4.5
A magnifying lens has a focal length of 100 mm. An object whose size is 16 mm is placed at some distance from the lens so that an image is formed at a distance of 25 cm in front of the lens.
What is the distance between the object and the lens?
An object of height 7 cm is kept at a distance of 25 cm in front of a concave mirror. The focal length of the mirror is 15 cm. At what distance from the mirror should a screen be kept so as to get a clear image? What will be the size and nature of the image?
Magnification for the convex mirror is ______.
Assertion: The focal length of the mirror is /and the distance of the object from the focus is V then the magnification of the mirror will be `("f"/"f−u")`
Reason: Magnification = `"image distance"/ "object distance"` = `(-"v"/"u")`
