# Analyzing Two Converging Lenses of the Same Focal Length

• luiseduardo
In summary, the conversation discusses the positioning and final image formation of two converging lenses with the same focal length and separated by 2f distance, with the second lens tilted at an angle of 60º. The options for the final image location are the optical centre of the first lens, the optical centre of the second lens, and a distance of f from both lenses. The correct answer is the optical centre of the first lens, which is at f/2 distance from the second lens. The student also questions the correctness of the solution and suggests the correct answer to be x = f/2 instead of 2f. The issue is resolved by tracing out a ray diagram and considering how a tilted lens should be treated.
luiseduardo

## Homework Statement

Two converging lenses of the same focal length f are separated by distance 2f. The axis of the second lens is inclined at angle θ = 60º with respect to the axis of the first lens. A parallel paraxial beam of light is incident from left side of the lens. Then:

(A) Final image after all possible refraction will formed at optical centre of first lens
(B) Final image after all possible refraction will formed at optical centre of second lens
(C) Final image after all possible refraction will formed at distance f from second lens
(D) Final image after all possible refraction will formed at distance f from first lens

f = p.p'/p+p'

## The Attempt at a Solution

Here the solution:

But, I don't agree with this line:

f/x = cos 60, but I think the correct is x/f = cos 60, so x = f/2. But the answer is 2f. Anyone could see if I'm wrong ?

You are right, the first image is at f/2 distance from the second lens.

ehild

Check by tracing out a ray diagram - the image from the first lens is the object for the second.
You can also see how your course notes tell you to treat the situation when a lens is tilted.

ehild said:
You are right, the first image is at f/2 distance from the second lens.

ehild

Thanks man.

I would suggest checking your calculations and equations to ensure accuracy. If you believe there is an error, it is important to double check and potentially consult with a colleague or reference materials. It is also important to consider the physical principles at play and how the light rays are being refracted through the lenses. Additionally, it may be helpful to sketch out a diagram of the setup to better understand the situation.

## 1. What is the purpose of analyzing two converging lenses of the same focal length?

The purpose of analyzing two converging lenses of the same focal length is to understand how they work together to produce a specific image. By analyzing their individual properties and how they interact with each other, scientists can predict the final image produced by the lenses.

## 2. How do you determine the focal length of a lens?

The focal length of a lens can be determined by measuring the distance between the lens and the point where the image comes into focus. This can be done by adjusting the distance between the lens and the object until the image is clear and sharp.

## 3. What is the relationship between the focal length and the image produced by a lens?

The focal length of a lens is directly related to the size and sharpness of the image it produces. A shorter focal length will result in a smaller image, while a longer focal length will produce a larger image. Additionally, a longer focal length will also produce a sharper image with less distortion.

## 4. How does the placement of the lenses affect the final image?

The placement of the lenses affects the final image by determining the magnification and clarity of the image. If the lenses are placed too far apart, the image may appear smaller and blurry. If they are placed too close together, the image may appear larger and distorted. The placement also affects the focal length of the combined lenses.

## 5. What factors can affect the performance of the lenses?

The performance of the lenses can be affected by several factors, such as the quality and curvature of the lenses, the distance between them, and any potential obstructions or imperfections in the path of light. Environmental factors such as temperature and humidity can also impact the performance of the lenses.

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