An object is 20cm from a convex lens and produce an image which is three times bigger than the object. What is the focal length of the lens?
To find the focal length of the lens, we can use the lens formula:
1/f = 1/v - 1/u
where:
f = focal length of the lens
v = image distance
u = object distance
Given:
u = 20 cm (object distance)
v = 3u (image distance)
Substituting the values into the lens formula:
1/f = 1/(3u) - 1/u
Simplifying the equation:
1/f = (1 - 3) / (3u)
1/f = -2 / (3u)
Now, substituting the value of u:
1/f = -2 / (3 * 20)
1/f = -2 / 60
1/f = -1/30
To find the focal length, we can take the reciprocal of both sides:
f = -30 cm
Since the focal length cannot be negative, we take the absolute value:
f = 30 cm
Therefore, the focal length of the convex lens is 30 cm.
Let's assume that the object distance from the lens is u, the image distance from the lens is v, and the magnification of the lens is M.
Given that the object distance (u) is 20 cm and the magnification (M) is 3, we can write the formula for magnification as:
M = -(v/u)
Rearranging the formula, we have:
v = -M*u
Plugging in the values, we get:
v = -(3)(20)
v = -60 cm
The lens equation for a convex lens is given by:
1/f = 1/v - 1/u
Plugging in the values, we have:
1/f = 1/(-60) - 1/20
Simplifying the equation, we get:
1/f = -3/60 - 1/20
1/f = -1/20 - 1/20
1/f = -2/20
1/f = -1/10
Taking the reciprocal of both sides, we get:
f = -10 cm
Since the focal length cannot be negative, the focal length of the lens is 10 cm.
To find the focal length of a convex 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 (distance of the image from the lens)
- u is the object distance (distance of the object from the lens)
In this case, we are given:
- u = -20 cm (as the object is 20 cm from the lens)
- The image produced is three times bigger than the object, so the image distance, v, will be positive.
Let's substitute the given values into the lens formula:
1/f = 1/v - 1/u
1/f = 1/v - 1/(-20)
1/f = 1/v + 1/20
Since the image is three times bigger than the object, it means the magnification, M, is equal to 3. The magnification is given by the formula:
M = v/u
3 = v/(-20)
v = -60 cm
Now we substitute the image distance, v, into the lens formula:
1/f = 1/v + 1/20
1/f = 1/(-60) + 1/20
Finding the reciprocal of both sides:
f = (-60 × 20) / (-60 + 20)
f = 1200 / (-40)
f = -30 cm
Therefore, the focal length of the lens is -30 cm.