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
Let's assume that the object distance is given by u, the image distance is given by v, and the focal length is given by f.
According to the magnification equation:
magnification (m) = -(v/u)
Given that the image is three times bigger than the object, the magnification is 3:
3 = -(v/u)
Solving for "v" in terms of "u":
v = -3u
Using the lens formula:
1/f = (1/v) - (1/u)
Substituting the values of v and u:
1/f = (1/-3u) - (1/u)
Simplifying the equation:
1/f = (-1 - 3)/(-3u)
1/f = (-4)/(-3u)
1/f = 4/(3u)
Rearranging the equation:
f = (3u)/4
Given that the object distance (u) is 20cm:
f = (3 * 20) / 4
f = 60 / 4
f = 15 cm
Therefore, the focal length of the convex lens is 15 cm.
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 from the lens
u = object distance from the lens
Given that the object is 20 cm from the lens, we have u = -20 cm (negative sign indicates it is on the same side as the object).
Let's assume the image distance v is positive since it's on the opposite side as the object.
We are also given that the image produced is three times bigger than the object. This implies that the image distance v is three times the object distance u:
v = 3u
Substituting the given values into the lens formula, we have:
1/f = 1/(3u) + 1/u
Simplifying the above equation:
1/f = 4/(3u)
Multiplying both sides by 3u:
3u/f = 4
Simplifying further:
u/f = 4/3
Therefore, the focal length f is:
f = (3u)/(4/3)
= 9u/4
= (9 * (-20))/4
= -45 cm
Hence, the focal length of the convex lens is -45 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 distance of the image from the lens, and u is the distance of the object from the lens.
Given:
u = 20cm (distance of the object from the lens)
The image is three times bigger, which means v = 3u (distance of the image from the lens)
Substituting these values into the lens formula:
1/f = 1/(3u) - 1/u
Simplifying the equation:
1/f = (1 - 3)/3u
1/f = -2/3u
To find the focal length (f), we need the value of u. Since u is given as 20cm, we can substitute this value:
1/f = -2/3(20)
1/f = -2/60
1/f = -1/30
Now, we can find the reciprocal of the right side to get f:
f = -30/1
f = -30cm
The focal length of the convex lens is -30cm. Note that the negative sign indicates that the lens is a convex lens, as convex lenses have positive focal lengths.