A divergent lens has focal length of 20 cm. At what distance should the object fromthe lens be placed so that an image is formed 10 cm away from the lens? What is themagnification produced, by the lens
Question
A divergent lens has focal length of 20 cm. At what distance should the object fromthe lens be placed so that an image is formed 10 cm away from the lens? What is themagnification produced, by the lens
Solution
The lens formula, which relates the object distance (u), the image distance (v), and the focal length (f) of a lens, is given by:
1/f = 1/v - 1/u
We know that for a divergent lens, the focal length is negative. So, f = -20 cm.
We also know that the image is formed 10 cm away from the lens. Since the image is formed on the same side as the object, the image distance is also negative. So, v = -10 cm.
Substituting these values into the lens formula, we get:
1/-20 = 1/-10 - 1/u
Solving this equation for u gives us:
1/u = 1/-20 - 1/-10 1/u = -1/20 + 1/10 1/u = -1/20 + 2/20 1/u = 1/20
So, u = 20 cm.
The object should be placed 20 cm from the lens.
The magnification (m) of the lens is given by the ratio of the image distance to the object distance:
m = -v/u
Substituting the known values gives us:
m = -(-10)/20 m = 10/20 m = 0.5
So, the magnification produced by the lens is 0.5. This means the image is half the size of the object.
Similar Questions
An object is placed at a distance of 20 cm from a convex lens of focal length 10 cm. The image is formed on the other side of the lens at a distance20 cm10 cm40 cm30 cm
A concave lens has focal length of 15 cm. At what distance should be object from the lens be placed so that it form an image at 10 cm from the lens?30 cm15 cm3 cm6 cm
An object is placed 70.3 cm to the left of a diverging lens. A virtual image is formed 12.9 cm to the left of the lens. Determine the focal length of the lens. Enter a – answer if appropriate.Focal Lengthcm
Same size of image is formed by a convex lens of focal length 20 cm . The distance betweenthe object and image is(a) 0 cm (b) 20 cm(c) 40 cm (d) 80 cm1
An object is placed 65.7 cm from a converging lens that has a focal length of 24.6 cm. Determine the image distance. Enter a – answer if appropriate.Image DistancecmInfoAttempts: 0/∞SubmitDetermine the magnification of this image. Enter a – answer if appropriate.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.