At what distance should an object be placed in front of a convex lens of focal length 20 cm to obtain an image of double its size
To determine the distance at which an object should be placed in front of a convex lens to obtain an image of double its size, 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 (in this case, twice the object size), and
u is the distance of the object from the lens.
First, let's express twice the size of the object as 2x. This means that the image distance v will be equal to 2x.
Now, let's substitute the given values into the lens formula:
1/f = 1/2x - 1/u.
We already know that the focal length f is 20 cm, so we can replace it:
1/20 = 1/2x - 1/u.
To find the distance u, we need to rearrange the equation:
1/u = 1/2x - 1/20.
Next, we simplify the equation by finding the common denominator:
1/u = (20 - 2x) / (2x * 20).
Now, we can find u by taking the reciprocal of both sides:
u = (2x * 20) / (20 - 2x).
Therefore, the object should be placed at a distance of (2x * 20) / (20 - 2x) from the convex lens of focal length 20 cm to obtain an image that is double the size of the object.