Solving Light and Lenses Questions: Focal Length, Magnification, Distance

[dranseth]

Homework Statement

1)A philatelist uses a magnifying glass with a focal length of 10cm. In order to examine a rare postage stamp, he holds the lens 4 cm from his eyes. If the distance for the most comfortable viewing of the image is 30cm from his eyes, how far from the lens must the postage stamp be placed? What will the magnification be?

2)A lens has a focal length of +20cm and a magnification of 4. How far apart are the object and the image?

Homework Equations

1/2) 1/f=1/Do+1/Di
Mag = hi/ho = -Di/Do

The Attempt at a Solution

I don't even know where to begin with the first question. I'm having difficulty interpreting it. Any help would be greatly appreciated.

 

[rl.bhat]

If the distance for the most comfortable viewing of the image is 30cm from his eyes, and the lens is at 4 cm from the eye, you have to keep the stamp at such distance from the lens that it forms the inage at 30cm - 4 cm = 26 cm from the lens. Now find the object distance.

 

[ogb p]

I would first clarify any confusion or uncertainty about the problem statement. In this case, it seems like the problem is asking for the distance from the lens to the postage stamp, as well as the magnification of the stamp when viewed through the lens.

To solve this problem, we can use the thin lens equation: 1/f = 1/do + 1/di, where f is the focal length, do is the distance of the object from the lens, and di is the distance of the image from the lens.

In this case, we are given that the focal length is 10cm and the distance for comfortable viewing is 30cm. We can set up the equation as follows:

1/10 = 1/4 + 1/di

Solving for di, we get a distance of 2.86cm. This means that the postage stamp should be placed 2.86cm away from the lens in order to be viewed comfortably.

To find the magnification, we can use the equation: mag = hi/ho = -di/do, where hi is the height of the image and ho is the height of the object.

Since we are not given the actual sizes of the object and image, we cannot calculate the magnification. However, we can say that the magnification will be negative since the image is being viewed through a magnifying glass, which produces an inverted image.

For the second question, we can use the same equations to solve for the distance between the object and the image. We are given that the focal length is +20cm and the magnification is 4. Plugging these values into the equation, we get:

1/20 = 1/do + 1/di

We can rearrange this equation to solve for di:

1/di = 1/20 - 1/do

Plugging in the magnification of 4, we get:

1/di = 1/20 - 1/(4*do)

Simplifying, we get:

1/di = (4-do)/20do

Solving for di, we get a distance of 5cm. This means that the object and image are 5cm apart when viewed through this lens.

In conclusion, by using the thin lens equation and the magnification equation, we can solve for the distances and magnifications in both of these scenarios. It is important to understand and use