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प्रश्न
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?
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उत्तर
Given Data:
- Object height (ho) = 7 cm
- Object distance (u) = −25 cm (since the object is in front of the concave mirror, it is taken as negative)
- Focal length (f) = −15 cm (concave mirror has a negative focal length)
Step 1: Find the Image Distance v
`1/f = 1/v + 1/u`
`1/v = 1/f - 1/u`
`1/v = 1/-15 - 1/-25`
`1/v = 1/-15 + 1/25`
`1/v = (-5+3)/75 = (-2)/75`
v = −37.5 cm
Step 2: Find the Size of the Image
Using the magnification formula:
`m = -v/u`
`m = -(-37.5)/-25`
= −1.5
Now, calculating the image height:
himage = m × hobject
himage = −1.5 × 7
= −10.5 cm
Step 3: Nature of the Image
- Since v is negative, the image is real and inverted.
- Since magnification ∣m∣ = 1.5 is greater than 1, the image is magnified.
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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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+4
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Reason: Magnification = `"image distance"/ "object distance"` = `(-"v"/"u")`
