Two lenses are in contact. One of the lenses has a focal length of +10.0cm when used alone. When the two are in combination, an object 20cm away from the lenses forms a real image 40cm away from the lenses. What is the focal length?
I am not sure how to approach this problem. I will like to see detailed steps on how to do this problem.
I tried using the formula 1/fe= 1/f1 + 1/f2
1/f=1/di+1/do
let do be at the original 20cm. Then those rays enter the second lens, and forms an image at 40cm
1/f=1/di+1/do
1/f=1/40+1/20=3/40
f= 40/3 cm
Poor nothing understood 😒😒😤😤😤😡😡😡
To solve this problem, you can use the lens formula:
1/f = 1/f1 + 1/f2
Where:
f1 is the focal length of the first lens,
f2 is the focal length of the second lens, and
f is the total focal length when the lenses are in combination.
We are given the following information:
f1 = +10.0 cm
The object is 20 cm away from the lenses and the image is formed 40 cm away from the lenses.
Let's break down the problem step by step:
1. From the given information, we know that the object distance (u) is 20 cm and the image distance (v) is 40 cm.
2. Substitute the values for u and v into the lens formula:
1/f = 1/u + 1/v
1/f = 1/20 + 1/40
3. Simplify the equation:
1/f = (2 + 1)/40
1/f = 3/40
4. Now, substitute the value of f1 into the equation:
1/f = 1/10 + 1/f2
4/40 = 3/40 + 1/f2
1/f2 = 4/40 - 3/40
1/f2 = 1/40
5. Take the reciprocal of both sides to find f2:
f2 = 40 cm
Now we have the value of f2, which is the focal length of the second lens when used alone.
To find the total focal length, f, when the lenses are in combination, substitute the values of f1 and f2 into the lens formula:
1/f = 1/f1 + 1/f2
1/f = 1/10 + 1/40
1/f = (4 + 1)/40
1/f = 5/40
f = 40/5 = 8 cm
Therefore, when the two lenses are in contact, the focal length is +8.0 cm.