Advertisements
Advertisements
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?
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.
APPEARS IN
संबंधित प्रश्न
A student has obtained an image of a well-illuminated distant object on a screen to determine the focal length, F1of the given spherical mirror. The teacher then gave him another mirror of focal length, F2 and asked him to obtain a focused image of the same object on the same screen. The student found that in order to focus the same object using the second mirror, he has to move the mirror away from the screen. From this observation, it may be concluded that both the spherical mirrors given to the student were (select the correct option)
(A) Concave and F1 < F2
(B) Concave and F1 > F2
(C) Convex and F1 < F2
(D) Convex and F1 > F2
What is the magnification of the images formed by plane mirrors and why?
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
The image formed by a concave mirror is virtual, erect and magnified. The position of object is:
(a) at focus
(b) between focus and centre of curvature
(c) at pole
(d) between pole and focus
What is the ratio of the height of an image to the height of an object known as?
Fill in the following blank with suitable word:
If the magnification has a plus sign, than image is ......... and.........
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?
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 ______.
Write down the magnification formula for a lens in terms of object distance and image distance. How does this magnification formula for a lens differ from the corresponding formula for a mirror?
An object is placed at a distance of 100 cm from a converging lens of focal length 40 cm.
(i) What is the nature of image?
(ii) What is the position of image?
A lens of focal length 20 cm is used to produce a ten times magnified image of a film slide on a screen. How far must the slide be placed from the lens?
An object placed 4 cm in front of a converging lens produces a real image 12 cm from the lens.
(a) What is the magnification of the image?
(b) What is the focal length of the lens?
(c) Draw a ray diagram to show the formation of image. Mark clearly F and 2F in the diagram.
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
An object is 0.09 m from a magnifying lens and the image is formed 36 cm from the lens. The magnification produced is:
(a) 0.4
(b) 1.4
(c) 4.0
(d) 4.5
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
The magnification produced by a spherical lens and a spherical mirror is + 2.0.
(a) The lens and mirror are both concave
(b) The lens and mirror are both convex
(c) The lens is convex but the mirror is concave
(d) The lens is concave but the mirror is convex
Assertion: The focal length of the mirror is /and the distance of the object from the focus is V then the magnification of the mirror will be `("f"/"f−u")`
Reason: Magnification = `"image distance"/ "object distance"` = `(-"v"/"u")`
What is the nature of the image formed by a concave mirror if the magnification produced by the mirror is +4?
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.
