Converging lens solve for all variables given f, Hi, and Ho

• Samr28
In summary, to find the distance to the coaster, we can use the equation 1/f = 1/do + 1/di and solve for do by multiplying through by do and substituting 1/M for di/do. This will give us the equation do/f = do/di + do/(1/M). From there, we can solve for do to find the distance to the coaster.
Samr28

Homework Statement

[/B]

What is directly given in the problem:
Converging lens with f=1.43m
Hi = 2m

Homework Equations

Hi/Ho = di/do
M = Hi/Ho = di/do
1/f = 1/do + 1/di

The Attempt at a Solution

Ho = 2m * 20 = 40m
Not sure how I can get do from this. All of the equations seem to need di.

Samr28 said:

Homework Statement

[/B]
View attachment 200090

What is directly given in the problem:
Converging lens with f=1.43m
Hi = 2m

Homework Equations

Hi/Ho = di/do
M = Hi/Ho = di/do
1/f = 1/do + 1/di

The Attempt at a Solution

Ho = 2m * 20 = 40m
Not sure how I can get do from this. All of the equations seem to need di.
You can get the object height from the magnification. Since the image is $20$ times smaller than the object, $M=1/20$. We also know that $H_i=2 \, m$.

To get the distance to the coaster, multiply $$\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}$$ through by $d_o$ and substitute $1/M=20$ for $d_o/d_i$. You know the focal length, so it shouldn't be difficult to solve for $d_o$ from there.

the image is 20x smaller than the object so

hi = 1/20 ho

giving us

hi/ho = 1/20

but hi/ho = di/do

so we also have that

di/do = 1/20

so that we have that the object distance in terms of the image distance is

do = ... ?

andrevdh said:
the image is 20x smaller than the object so

hi = 1/20 ho

giving us

hi/ho = 1/20

but hi/ho = di/do

so we also have that

di/do = 1/20

so that we have that the object distance in terms of the image distance is

do = ... ?
Multiply the equation $$\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}$$ through by $d_o$. This gives you the equation $$\frac{d_o}{f}=\frac{d_o}{d_o}+\frac{d_o}{d_i}$$ $d_o/d_o=1$ and $d_o/d_i=1/M$ Solve for the remaining $d_o$.

1. What is a converging lens?

A converging lens is a type of lens that is thicker in the middle and thinner at the edges. It is also known as a convex lens. This type of lens is used to bring parallel rays of light together to a single point, known as the focal point.

2. What is the focal length of a converging lens?

The focal length of a converging lens is the distance from the center of the lens to the focal point. It is represented by the letter 'f' and is measured in meters (m).

3. What is the difference between Ho and Hi in the formula for converging lens?

In the formula for a converging lens, Ho represents the object height, which is the height of the object being viewed. Hi represents the image height, which is the height of the image formed by the lens.

4. How do I solve for all variables given f, Hi, and Ho?

To solve for all variables in the formula for a converging lens, you can use the equation: 1/f = 1/Hi + 1/Ho. Plug in the values for f, Hi, and Ho and solve for the remaining variable. Remember to use the correct units for each variable.

5. Can a converging lens have a negative focal length?

Yes, a converging lens can have a negative focal length. A negative focal length means that the focal point is located on the opposite side of the lens from where the light is coming from. This is known as a virtual image, where the light rays do not actually converge at a point, but appear to be coming from a specific point when viewed through the lens.

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