# Find the refractive index for the lens and find the image distance

• Karl Karlsson
In summary, the problem involves a thin lens with upper and lower radii of curvature, a focal distance, and a refractive index for air and water. The goal is to calculate the refractive index for the glass and the distance below the water surface where the image of a distant object will end up. The solution involves using the known values for the refractive indices of air and water, as well as the given values for the focal distance and radii of curvature, to determine the refractive index of the glass and the distance below the water surface. The answer can be expressed in terms of the given symbols and the refractive index for water.
Karl Karlsson
Homework Statement
A thin lens has an upper radius of curvature đť‘…1 and a lower radius of curvature đť‘…2. When the lens is completely surrounded by air, it has a focal distance đť‘“. The lens is then placed in the interface between air and water inside a vessel (see figure). Calculate the refractive index for the glass and the distance below the water surface on which the image of a distant object will end up?
Relevant Equations
A thin lens has an upper radius of curvature đť‘…1 and a lower radius of curvature đť‘…2. When the lens is completely surrounded by air, it has a focal distance đť‘“. The lens is then placed in the interface between air and water inside a vessel (see figure). Calculate the refractive index for the glass and the distance below the water surface on which the image of a distant object will end up?
A thin lens has an upper radius of curvature đť‘…1 and a lower radius of curvature đť‘…2. When the lens is completely surrounded by air, it has a focal distance đť‘“. The lens is then placed in the interface between air and water inside a vessel (see figure). Calculate the refractive index for the glass and the distance below the water surface on which the image of a distant object will end up?

The refractive index for water is given to nc = 1.33 and for air na = 1.00

My attempt:

Is my solution correct? I have nowhere to check the answer and I have not done any similar problem before. Have I missed something?

Last edited:
Your work looks good to me. But, they might want you to express the final answer in terms of the givens: ##f##, ##R_1##, ##R_2##, ##n_{air}##, and ##n_{water}##.

TSny said:
Your work looks good to me. But, they might want you to express the final answer in terms of the givens: ##f##, ##R_1##, ##R_2##, ##n_{air}##, and ##n_{water}##.
I assumed the refractive index for water was given because I could not solve the problem without it. Can the problem be solved if one only knows the refractive index for air?

Karl Karlsson said:
I assumed the refractive index for water was given because I could not solve the problem without it. Can the problem be solved if one only knows the refractive index for air?
You can assume ##n_{water}## to be known. But since no numerical values are given in the statement of the problem, I don't think you will need to use a particular value for ##n_{water}##.

I think they want you to express your answers in terms of the symbol ##n_{water}## as well as the given symbols ##R_1##, ##R_2##, and ##f##. Here, ##f## is the focal length with air on both sides of the lens.

For the first question, you found the index of refraction of the glass in terms of these symbols and it looks right.

Your answer to the second question also looks correct to me. But I was wondering if you are expected to express your answer in terms of only the "given" symbols ##R_1##, ##R_2##, and ##f## (as well as ##n_{water}##). It could be that the way you expressed the answer is completely adequate. It depends on your instructor.

Karl Karlsson

## What is the refractive index for a lens?

The refractive index for a lens is a measure of how much a lens bends or refracts light. It is typically denoted by the letter "n" and is a dimensionless number.

## How do you find the refractive index for a lens?

The refractive index for a lens can be found by dividing the speed of light in a vacuum by the speed of light in the material of the lens. This can be calculated using the formula n=c/v, where c is the speed of light in a vacuum and v is the speed of light in the lens material.

## What factors affect the refractive index of a lens?

The refractive index of a lens can be affected by several factors, including the material of the lens, the wavelength of light passing through the lens, and the temperature of the lens.

## How does the refractive index of a lens affect the image distance?

The refractive index of a lens plays a crucial role in determining the image distance. In general, a higher refractive index will result in a shorter image distance, while a lower refractive index will result in a longer image distance.

## What is the relationship between the refractive index and the power of a lens?

The refractive index and the power of a lens are inversely proportional. This means that as the refractive index increases, the power of the lens decreases, and vice versa. The power of a lens can be calculated using the formula P=1/f, where P is the power of the lens and f is the focal length.

Replies
7
Views
2K
Replies
3
Views
999
Replies
3
Views
647
Replies
2
Views
1K
Replies
3
Views
2K
Replies
1
Views
1K
Replies
2
Views
2K
Replies
9
Views
2K
Replies
5
Views
412
Replies
8
Views
5K