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प्रश्न
The focal length of a concave lens is 20 cm. At what distance from the lens should a 5 cm tall object be placed so that its image is formed at a distance of 15 cm from the lens? Also calculate the size of the image formed.
उत्तर
Focal length of concave lens, f = −20 cm
Distance of the image from the lens, v = -15 cm
Using the lens formula, we get:
`1/f=1/v - 1/u`
`1/-20= 1/-15 - 1/u`
`1/u=1/-15-1/-20`
`1/u=(-4+3)/60 = (-1)/60`
`u=-60 "cm"`
To find the size of the image formed (h′), use the magnification formula, where magnification (m) = `h^'/h = v/u` and h is the height of the object.
h=5 cm, and we have v = -15 cm and u = -60 cm
`m = (-15)/-60=1/4`
`h^' = mxxh = 1/4xx5 =1.25`
Hence, the size of the image is 1.25 cm.
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संबंधित प्रश्न
A student is using a convex lens of focal length 10 cm to study the image formation by a convex lens for the various positions of the object. In one of his observations, he may observe that when the object is placed at a distance of 20 cm from the lens, its image is formed at (select the correct option)
(A) 20 cm on the other side of the lens and is of the same size, real and erect.
(B) 40 cm on the other side of the lens and is magnified, real and inverted.
(C) 20 cm on the other side of the lens and is of the same size, real and inverted.
(D) 20 cm on the other side of the lens and is of the same size, virtual and erect.
The image formed by a spherical mirror is real, inverted and is of magnification -2. If the image is at a distance of 30 cm from the mirror, where is the object placed? Find the focal length of the mirror. List two characteristics of the image formed if the object is moved 10 cm towards the mirror.
A spherical mirror produces an image of magnification -1 on a screen placed at a distance of 50 cm from the mirror.
(a) Write the type of mirror.
(b) Find the distance of the image from the object.
(c) What is the focal length of the mirror?
(d) Draw the ray diagram to show the image formation in this case.
A student was asked by his teacher to find the image distance for various object distance in case of a given convex lens. He performed the experiment with all precautions and noted down his observations in the following table:
| S. No. |
Object distance (cm) |
Image distance (cm) |
| 1 | 60 | 15 |
| 2 | 48 | 16 |
| 3 | 36 | 21 |
| 4 | 24 | 24 |
| 5 | 18 | 36 |
| 6 | 16 | 48 |
After checking the observations table the teacher pointed out that there is a mistake in recording the image distance in one of the observations. Find the serial number of the observations having faulty image distance.
(A) 2
(B) 3
(C) 5
(D) 6
The image seen in a plane mirror cannot be formed on a screen. What name is given to this type of image?
Linear magnification (m) produced by a rear view mirror fitted in vehicles:
(a) is equal to one
(b) is less than one
(c) is more than one
(d) can be more less than one depending on the position of object
Explain what is meant by a virtual, magnified image.
The lens A produces a magnification of, − 0.6 whereas lens B produces a magnification of + 0.6.
What is the nature of lens A?
At which position will you keep an object in front of a convex lens so as to get a real image of the same size as the object? Draw a figure.
