A 24mm high object is 15cm in front of a +10cm concave lens . 24cm behind the convex lens is a -10cm concave lens . Calculate the size of the final object.
To calculate the size of the final object, we need to consider the image formed by each lens and the magnification produced by each lens.
Let's break down the problem step by step:
Step 1: Determine the image formed by the first lens (convex lens).
Given:
Object height (h₁) = 24mm (0.024cm)
Object distance from the lens (u₁) = -15cm (since it is in front of the lens)
Using the lens formula (1/f = 1/v - 1/u), we can find the image distance (v₁) formed by the convex lens:
1/f₁ = 1/v₁ - 1/u₁
Since we are given the focal length (f₁) as +10cm, we can substitute it into the equation:
1/10 = 1/v₁ - 1/-15
Solving this equation will give us the value of v₁, which represents the image distance formed by the first lens.
Step 2: Determine the image formed by the second lens (concave lens).
Given:
Image distance formed by the first lens (v₁)
The first lens creates an image, and that image becomes the object for the second lens. The distance from the second lens to this image is:
Object distance from the second lens (u₂) = 24cm - v₁
Using the lens formula (1/f = 1/v - 1/u), we can find the image distance (v₂) formed by the second lens:
1/f₂ = 1/v₂ - 1/u₂
The focal length (f₂) given is -10cm (negative because it is a concave lens).
Step 3: Calculate the magnification produced by each lens.
For the first lens:
Magnification (m₁) = Image height (h₁') / Object height (h₁)
We know the object height (h₁), and with the knowledge of the image distance (v₁), we can calculate the image height (h₁') using the magnification formula.
For the second lens:
Magnification (m₂) = Image height (h₂') / Object height (h₁')
Again, we can calculate the image height (h₂') using the magnification formula and the known object height (h₁') and image distance (v₂).
Finally, the size of the final object can be determined by multiplying the object height (h₁) by the magnification produced by the second lens (m₂).
Note: It would be helpful to know the focal lengths of the lenses to proceed with the calculations.