Advertisements
Advertisements
Question
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?
Solution
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.
APPEARS IN
RELATED QUESTIONS
A student wants to project the image of a candle flame on a screen 90 cm in front of a mirror by keeping the flame at a distance of 15 cm from its pole.
(a) Suggest the type of mirror he should use.
(b) Determine the linear magnification in this case.
(c) Find the distance between the object and its image.
(d) Draw ray diagram to show the image formation in this case
What is the magnification of the images formed by plane mirrors and why?
What sign (+ve or −ve) has been given to the following on the basis of Cartesian Sigh Convention?
Height of a real image.
What is the nature of image formed by a concave mirror if the magnification produced by the mirror
−2?
A virtual, erect and magnified image of an object is to be obtained with a convex lens. For this purpose,the object should be placed:
(a) between 2F and infinity
(b) between F and optical centre
(c) between F and 2F
(d) at F
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?
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:
20 cm from the lens?
Linear magnification produced by a convex lens can be:
(a) less than 1 or more than 1
(b) less than 1 or equal to 1
(c) more than 1 or equal to 1
(d) less than 1, equal to 1 or more than 1
In order to obtain a magnification of, –3 (minus 3) with a convex lens, the object should be placed:
(a) between optical centre and F
(b) between F and 2F
(c) at 2F
(d) beyond 2F
If a magnification of, –1 (minus 1) is obtained by using a converging lens, then the object has to be placed:
(a) within f
(b) at 2f
(c) beyond 2f
(d) at infinity
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
If a magnification of, –1 is to be obtained by using a converging lens of focal length 12 cm, then the object must be placed:
(a) within 12 cm
(b) at 24 cm
(c) at 6 cm
(d) beyond 24 cm
In order to obtain a magnification of, –0.75 with a convex lens of focal length 8 cm, the object should be placed:
(a) at less than 8 cm
(b) between 8 cm and 16 cm
(c) beyond 16 cm
(d) at 16 cma
A magnifying lens has a focal length of 100 mm. An object whose size is 16 mm is placed at some distance from the lens so that an image is formed at a distance of 25 cm in front of the lens.
Where should the object be placed if the image is to form at infinity?
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?
The power of a lens is +4D. Find the focal length of this lens. An object is placed at a distance of 50 cm from the optical centre of this lens. State the nature and magnification of the image formed by the lens and also draw a ray diagram to justify your answer.
