In what position will a converging lens of local length 10 cm from an image of luminous object on a screen located 50 cm from the object.
To determine the position of the image formed by a converging lens, we can use the lens formula:
1/f = 1/v - 1/u,
where:
f is the focal length of the lens,
v is the image distance from the lens, and
u is the object distance from the lens.
Given that the focal length (f) of the converging lens is 10 cm and the object distance (u) is 50 cm, we can plug these values into the lens formula:
1/10 = 1/v - 1/50.
To find the position of the image (v), we need to solve this equation. Let's simplify it step by step:
Multiply both sides of the equation by 50v to eliminate denominators:
50v/10 = 50v/v - 50v/50.
Simplify:
5v = 50 - v.
Add v to both sides:
5v + v = 50.
Combine like terms:
6v = 50.
Divide both sides by 6 to solve for v:
v = 50/6.
So, the image distance (v) is approximately 8.33 cm.
Now, to determine the position of the image, we need to know whether the image is formed on the same side or opposite side of the lens as the object.
Since the given lens is a converging lens, the image will be formed on the opposite side of the object. Therefore, the position of the image is 8.33 cm from the lens on the opposite side as the object.