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प्रश्न
A convex mirror has a focal length of 18 cm. The image of an object kept in front of the mirror is half the height of the object. What is the distance of the object from the mirror?
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उत्तर
Given:
Focal length (f) = 18 cm
Magnifiction (M) = `("Height of the image" ("h"_2))/("Height of the object" ("h"_1))`
= `1/2`
Find: Object distance (u)
Formula:
- M = `("h"_2)/("h"_1) = -"v"/"u"`
- `1/"f" = 1/"v" + 1/"u"`
Calculations:
According to formula (i),
`1/2 = -"v"/"u"`
∴ v = `-"u"/2`
According to formula (ii),
`1/"f" = 1/"v" + 1/"u" = ("u" + "v")/("uv")`
∴ f = `("uv")/ ("u" + "v")`
Now, v = `-"u"/2`
∴ f = `("u"((-"u")/2))/("u" + ((-"u")/2))`
∴ `18 = ((-"u"^2)/2)/((2"u" - "u")/2) = (-"u"^2)/"u"`
∴ u = −18 cm
A negative sign indicates that the object is placed to the left of the mirror.
Hence, the distance of the object from the mirror is 18 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
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