Solving a Physics Magnification Problem with a 6cm Focal Length Magnifier

[disk256]

1. The fine print in a contract that you want to read is 1 mm tall. You have a magnifier with a focal length of 6 cm. Where must you hold the magnifier so that the image appears to be 1 cm tall. Where is the image located



2. m= -di/do



3. using the equation given above i tried to use the equation hi/ho= di/do but no value for dO is given which means i can't use the equation


help would be appericiated

 

[rl.bhat]

Using this equation hi/ho= di/do find di in terms of do. ho and hi. Use the formula which related the f, do and di to get the required answer.

 

[nlightner]

I would suggest using the thin lens equation, which is 1/f = 1/do + 1/di, where f is the focal length, do is the object distance, and di is the image distance. We can rearrange this equation to solve for di, which is the distance of the image from the lens.

Since we are given the focal length (f = 6 cm) and we want to find the distance of the image when the object is 1 cm tall (hi = 1 cm), we can plug these values into the equation and solve for di.

1/6 = 1/do + 1/di

Rearranging, we get:

di = 1/(1/6 - 1/do)

Now, we need to find the object distance (do) in order to solve for di. We know that the object size (ho) is 1 mm and we want the image size (hi) to be 1 cm. Using the magnification equation (m = -di/do), we can set up the following:

-1 = -di/do

Solving for do, we get:

do = di

This means that the object distance and image distance are equal, so we can substitute do with di in the thin lens equation:

di = 1/(1/6 - 1/di)

di = 1/(1/6 - 1/di)

Multiplying both sides by di, we get:

di^2 = 1/6 - 1/di

Now, we can solve for di by using the quadratic formula:

di = (1 ± √(1 - 4(1/6)(-1)))/2(1/6)

di = (1 ± √(1 + 2/3))/1/3

di = (1 ± √(5/3))/1/3

di = (1 ± √5)/1/3

di = (1 ± 2.236)/1/3

di = 3.236/1/3 or -1.236/1/3

di = 9.708 cm or -3.708 cm

Since we are looking for a positive value for di, we can discard the negative solution. This means that the image is located 9.708 cm from the lens. Therefore, you should hold the magnifier 9