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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
The height of the image formed by an object of height 10 cm placed in front of a plane mirror is __________.
(a) 5 cm
(b) 10 cm
(c) 15 cm
(d) 20 cm
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Give two circumstances in which a concave mirror can form a magnified image of an object placed in front of it. Illustrate your answer by drawing labelled ray diagrams for both.
The image formed by a concave mirror is real, inverted and of the same size as the object. The position of the object must then be:
(a) at the focus
(b) between the centre of curvature and focus
(c) at the centre of curvature
(d) beyond the centre of curvature
A virtual, erect and magnified image of an object is to be produced with a concave mirror of focal length 12 cm. Which of the following object distance should be chosen for this purpose?
(i) 10 cm
(ii) 15 cm
(iii) 20 cm
Give reason for your choi
What sign (+ve or −ve) has been given to the following on the basis of Cartesian Sigh Convention?
Height of a virtual image.
Write down a formula for the magnification produced by a concave mirror.
in terms of object distance and image distance
When an object is placed 20 cm from a concave mirror, a real image magnified three times is formed. Find:
(a) the focal length of the mirror.
(b) Where must the object be placed to give a virtual images three times the height of the object?
A dentist's mirror has a radius of curvature of 3 cm. How far must it be placed from a small dental cavity to give a virtual image of the cavity that is magnified five times?
An object 20 cm from a spherical mirror gives rise to virtual image 15 cm behind the mirror. Determine the magnification of the image and the type of mirror used.
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 ______.
When an object is placed at a distance of 36 cm from a convex lens, an image of the same size as the object is formed. What will be the nature of image formed when the object is placed at a distance of:
10 cm from the lens?
Determine how far an object must be placed in front of a converging lens of focal length 10 cm in order to produce an erect (upright) image of linear magnification 4.
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
To obtain a magnification of, –0.5 with a convex lens, the object should be placed:
(a) at F
(b) between optical centre and F
(c) between F and 2F
(d) beyond 2F
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?
Magnification for the convex mirror is ______.
A negative sign in the value of magnification indicates that the image is ______.
