# Thin Lenses Problem: Solving for $q=d-p$

• Archimedess
In summary, the thin lens equation is a mathematical equation that relates the focal length of a lens to the object and image distances. It can be used to solve for q by rearranging the equation. There are two types of lenses, converging and diverging, which cause light rays to converge and diverge, respectively. The object and image distances can be determined using a ruler or the thin lens equation. The equation can be used for both types of lenses, but for diverging lenses, the focal length and image distance are considered negative. The position of the object relative to the lens affects the type and location of the image formed.
Archimedess
Homework Statement
We try with a thin convergent lens, by moving it on its optical axis, to project on a fixed screen the image of a small object located in the optical axis. This is only possible with two position of the lens ##I_1=20cm## and ##I_2=80cm##. Determine the ##d## distance from the object to the screen and focal length ##f## of the lens.
Relevant Equations
##\frac{1}{p}+\frac{1}{q}=\frac{1}{f}##
##d=q+p##

Where ##p## is the distance of the object from the lens and ##q## is the distance between the image and the lens.
Since ##d=q+p \implies q=d-p##
\begin{cases}
\frac{1}{I_1}+\frac{1}{d-I_1}=\frac{1}{f}\\
\frac{1}{I_2}+\frac{1}{d-I_2}=\frac{1}{f}
\end{cases}

Is this correct?

Yes. Now manipulate until you have an expression for ##d##.

## 1. What is a thin lens?

A thin lens is a transparent optical device with two curved surfaces that are designed to refract light in a specific way. It is typically made of glass or plastic and is used to focus or diverge light rays.

## 2. What is the "q=d-p" equation used for?

The "q=d-p" equation is used to solve for the image distance (q) of a thin lens, given the object distance (d) and the focal length (p) of the lens. This equation is derived from the thin lens equation, 1/q = 1/p + 1/d, which relates the object distance, image distance, and focal length of a thin lens.

## 3. How do you solve for q in the "q=d-p" equation?

To solve for q, you simply need to substitute the known values for d and p into the equation and solve for q using basic algebraic principles. Make sure to pay attention to the units of measurement and use consistent units throughout the calculation.

## 4. What are the units for q, d, and p in the "q=d-p" equation?

The units for q, d, and p in the "q=d-p" equation are all in distance units, typically meters (m) or centimeters (cm). It is important to use consistent units throughout the equation to ensure accurate calculations.

## 5. Are there any assumptions or limitations when using the "q=d-p" equation?

Yes, the "q=d-p" equation assumes that the thin lens is being used in air and that the light rays are parallel to the optical axis of the lens. It also assumes that the lens is thin, meaning that its thickness is negligible compared to its radius of curvature. Additionally, this equation is only applicable to thin lenses and may not accurately predict the behavior of thick lenses or other optical devices.

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