Advertisements
Advertisements
Question
An object is placed (a) 20 cm, (b) 4 cm, in front of a concave mirror of focal length 12 cm. Find the nature and position of the image formed in each case.
Solution
Case (a)
Distance of the object from the mirror (u) = -20 cm
The focal length of the concave mirror (f) = -12 cm
We have to find the distance of the image (v).
Using the magnification formula, we get
`1/f=1/v+1/u`
so
`or 1/-12=1/v+1/-20`
`1/-12=1/v-1/20`
`or 1/20-1/12=1/v`
`or(3-5)/60=1/v`
`or -2/60=1/v`
`or v= 60/-2`
`v=-30` cm
The image will be at a distace of 30 cm in front of mirror.Again,
Magnification `(m)=(-v)/u `
`m=-(-30)/-20=-1.5`
Therefore, the image will be real, inverted and enlarged.
Thus the image is real, inverted and enlarged.
Case B
Distance of the object from the mirror (u) = -4 cm
The focal length of the concave mirror (f) = -12 cm
We have to find the distance of the image (v).
Using the mirror formula, we get
`1/f=1/v+1/u`
`1/-12=1/v+1/-4`
`or 1/4-1/12=1/v`
`or(3-1)/12=1/v`
`or 2/12=1/v`
Therefore, distance of image (v) is 6 cm.Now, using the magnification formula, we get
`m=-v/u`
`m=-6/-4=1.5`
Thus, the image is virtual and erect.
APPEARS IN
RELATED QUESTIONS
A converging lens has focal length of 12 cm. Calculate at what distance the object should be placed from the lens so that it forms an image at 48 cm on the other side of the lens.
A student has obtained a point image of a distant object using the given convex lens. To find the focal length of the lens he should measure the distance between the :
(A) lens and the object only
(B) lens and the screen only
(C) object and the image only
(D) lens and the object and also between the object and the image
The image of a candle flame placed at a distance of 30 cm from a spherical lens is formed on a screen placed on the other side of the lens at a distance of 60 cm from the optical centre of the lens. Identify the type of lens and calculate its focal length. If the height of the flame is 3 cm, find the height of its image.
If a magnification of, −1 (minus one) is to be obtained by using a converging mirror, then the object has to be placed:
(a) between pole and focus
(b) at the centre of curvature
(c) beyond the centre of curvature
(d) at infinity
In order to obtain a magnification of, −1.5 with a concave mirror of focal length 16 cm, the object will have to be placed at a distance
(a) between 6 cm and 16 cm
(b) between 32 cm and 16 cm
(c) between 48 cm and 32 cm
(d) beyond 64 cm
The image of a candle flame placed at a distance 30 cm from a spherical lens is formed on a screen placed at a distance of 60 cm from the lens. Identify the type of lens and calculate its focal length. If the height of the flame is 2.4 cm, find the height of its image.
The image of a candle flame formed by a lens is obtained on a screen placed on the other side of the lens. If the image is three times the size of the flame and the distance between lens and image is 80 cm, at what distance should the candle be placed from the lens? What is the nature of the image at a distance of 80 cm and the lens?
In a reading glass what is the position of the object with respect to the convex lens used?
The magnification by a lens is -3. Name the lens and state how are u and v related?
What information about the nature of image is erect or inverted, do you get from the sign of magnification + or -?
