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प्रश्न
An object is 24 cm away from a concave mirror and its image is 16 cm from the mirror. Find the focal length and radius of curvature of the mirror, and the magnification of the image.
उत्तर
Distance of object (u) = -24 cm
Distance of image (v) = -16 cm
We have to find the focal length of the mirror (f) and the magnification of the image (m).
Using the mirror formula, we get
`1/f=1/u+1/v`
`1/f=1/-24+1/-16`
`or 1/f=(-2-3)/48`
`or 1/f=(-5)/48`
`or f=-48/5`
`f=-9.6` cm
Therefore, the focal length of the concave mirrio is 9.6
R adius of curvature (R)=2f
`R=2xx-9.6`
`R=-19.2 cm`
Therefore, the radius of curvature of the mirror is 19.2 cm
Now, using the magnification formula, we get
`m =(-v)/u`
`m=(-16)/-24`
m=0.66
Thus, the image is real, inverted and small in size.
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संबंधित प्रश्न
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State whether the following statement is True or False
The sides of an object and its image formed by a concave mirror are always interchanged.
A student took three concave mirrors of different focal lengths and performed the experiment to see the image formation by placing an object at different distance with these mirrors as shown in the following table.
| Case No. | Object-distance | Focal length |
| I | 45 cm | 20 cm |
| II | 30 cm | 15 cm |
| III | 20 cm | 30 cm |
Now answer the following questions:
(a) List two properties of the image formed in Case I.
(b) In which one of the cases given in the table, the mirror will form real image of same size and why?
(c) Name the type of mirror used by dentists. Given reason why do they use such type of mirrors.
OR
(c) Look at the table and identify the situation (object distance and focal length) which resembles the situation in which concave mirrors are used as shaving mirrors? Draw a ray diagram to show the image formation in this case.
