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प्रश्न
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.
उत्तर
Focal length = `1/"P"= 1/4` = 0.25 m or 25 cm. It is a convex lens as power and focal length are positive.
Focal length, f = +25 cm
Object distance, u = -50 cm
Image distance, v = ?
Image height, I = ?
Using lens formula,
`1/"f"=1/"v"-1/"u"`
`1/25=1/"v"-1/((-50))`
`1/25 + 1/((-50)) =1/"v"`
`(2 - 1)/50 =1/"v"`
`1/"v" = 1/50`
v = +50 cm
Also, magnification, m = `"v"/"u"`
Hence, m = `((50))/-(50)= -1`
Image formation occurs thus 50 cm in front of the lens. Due to a magnification of 1, the image is the same size as the object. The image is inverted as evidenced by the negative magnification.
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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?
Where should an object be placed in front of the concave mirror so as to obtain its virtual, erect and magnified image?
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
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.
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?
The filament of a lamp is 80 cm from a screen and a converging lens forms an image of it on a screen, magnified three times. Find the distance of the lens from the filament and the focal length of the lens.
What is the nature of the image formed by a concave mirror if the magnification produced by the mirror is +4?
