What should be the focal length of a double concave length 60 that an object placed 25 cm from it will produce 3/4 times large as the object?
To find the focal length of a double concave lens, we can use the lens formula:
1/f = (1/v) - (1/u),
where f is the focal length, v is the image distance, and u is the object distance.
Given:
Object distance (u) = -25 cm (negative sign denotes object is placed on the same side as the incident light)
Image distance (v) = -3/4 times the object size
Let's substitute these values into the lens formula:
1/f = (1/(-3/4u)) - (1/u),
Simplifying the equation:
1/f = (-4/3u) - (3/3u) = (-7/3u),
Taking the reciprocal of both sides:
f = -3u/7.
Now, we have the equation for the focal length in terms of object distance.
Given an object distance (u) = -60 cm (since the focal length is negative for a double concave lens), we can calculate the focal length as follows:
f = -3u/7 = -3(-60)/7 = 180/7 ≈ 25.71 cm.
Therefore, the focal length of the double concave lens should be 25.71 cm.