In an experiment ,an object was placed on the principal axis of a convex lens 25 centimetres away from the lens. Areal image 4 times the size of the object was obtained. The focal length of the lens is?
We can use the magnification formula:
m = -v/u
where m is the magnification, v is the image distance, and u is the object distance.
We are given that the image is 4 times the size of the object, so m = 4. We are also given that the object is 25 cm away from the lens, so u = -25 cm (since the object is in front of the lens, the distance is negative). Finally, we want to find the focal length f of the lens.
Using the lens formula:
1/f = 1/v - 1/u
We can rearrange to solve for v:
1/v = 1/f + 1/u
1/v = 1/f - 1/25
v = 25f / (f-25)
Now we can substitute this into the magnification formula and solve for f:
4 = -v/u
4 = -25f / u(f-25)
4 = -25f / (-25)(f-25)
4 = f / (f-25)
4f - 100 = f
3f = 100
f = 33.33 cm
Therefore, the focal length of the lens is approximately 33.33 cm.
To find the focal length of the 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
u is the object distance from the lens
Given:
Object distance, u = -25 cm (negative sign indicates object is placed on the same side as the incident rays, i.e., left side of the lens)
Image distance, v = -4u (as the image is 4 times the size of the object, it indicates a magnification of +4)
Now, substitute the given values into the lens formula:
1/f = 1/(-4u) - 1/u
1/f = (-1/4u - 1/u)
1/f = (-1 - 4)/4u
1/f = -5/4u
Thus, the focal length of the convex lens can be calculated by taking the reciprocal of both sides:
f = -4u/5
Substituting the value of u:
f = -4(-25)/5
f = 100/5
f = 20 cm
Therefore, the focal length of the convex lens is 20 cm.