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प्रश्न
An object of height 5 cm is placed perpendicular to the principal axis of a concave lens of focal length 10 cm. If the distance of the object from the optical centre of the lens is 20 cm, determine the position, nature and size of the image formed using the lens formula.
उत्तर
Given:-
Height of the object = h = 5 cm
Focal length of the concave lens = f = −10 cm
Object distance = u = −20 cm
Using the lens formula, we get
`1/"f"=1/"v"-1/"u"`
`therefore1/"v"=1/"f"+1/"u"=1/(-10)-1/20=(-2-1)/20=(-3)/20`
`therefore"v"=-6.67cm`
Hence, the image is formed 6.67 cm in front of the lens on the same side as the object.
Because v is negative, we can say that the image is virtual.
From the magnification formula for the lens, we get
`"m"=(h')/h="v"/"u"`
`thereforeh'="vh"/"u"=(-6.67xx5)/-20=1.67cm`
Hence, the size of the image is h′ = 1.67 cm.
Because the height of the image is positive and smaller than the height of the object, the image is erect and diminished.
So, we can conclude that the image is virtual, erect and diminished.
संबंधित प्रश्न
To construct a ray diagram we use two rays of light which are so chosen that it is easy to determine their directions after reflection from the mirror. Choose these two rays and state the path of these rays after reflection from a concave mirror. Use these two rays to find the nature and position of the image of an object placed at a distance of 15 cm from a concave mirror of focal length 10 cm.
For what position of an object, a concave mirror forms a real image equal in size to the object?
The focal length of a small concave mirror is 2.5 cm. In order to use this concave mirror as a dentist's mirror, the distance of tooth from the mirror should be:
(a) 2.5 cm
(b) 1.5 cm
(c) 4.5 cm
(d) 3.5 cm
Write down a formula for the magnification produced by a concave mirror.
in terms of height of object and height of image
An object of 5.0 cm size is placed at a distance of 20.0 cm from a converging mirror of focal length 15.0 cm. At what distance from the mirror should a screen be placed to get the sharp image? Also calculate the size of the image.
If the image formed is always virtual, the mirror can be:
(a) concave or convex
(b) concave or plane
(c) convex or plane
(d) only convex
The mirror which can form a magnified image of an object is:
(a) convex mirror
(b) plane mirror
(c) concave mirror
(d) both convex and concave mirror
In which equipment/s do you find ___________________
Large ______ mirrors are used to concentrate sunlight to produce heat in solar furnaces.
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.
