Finding the Optimal Lens Position for a Sharp Image of a Candle

[roncool11]

A candle is placed 1.8 m from a screen. whereshould a lens of focus length 21 cm (0.21 m) be placed between the screen and the candle to prduce a sharp image screen?

The only formula i could think of was 1/f=1/do+1/di



I've now spent 3 hours on this (test tomorrow) and still don't know where to start. I have that first formula and the only other formula we've used had to do with magnification and object height. I am truly lost.

 

[LowlyPion]

Welcome to PF.

Looks like the thin lens formula applies here doesn't it?

So ... won't the distance x be able to be found by

1/x + 1/(1.8 - x) = 1/.21 ?

 

[thomate1]

I understand your frustration and the importance of finding the optimal lens position for a sharp image of a candle. To solve this problem, we can use the thin lens equation, which is 1/f = 1/do + 1/di, where f is the focal length of the lens, do is the distance from the object (candle) to the lens, and di is the distance from the lens to the image (screen).

In this case, we know that the focal length of the lens is 0.21 m and the distance from the candle to the screen is 1.8 m. We can plug these values into the equation and solve for di, which will give us the distance from the lens to the screen where a sharp image will be produced.

1/0.21 = 1/1.8 + 1/di

4.76 = 0.56 + 1/di

1/di = 4.76 - 0.56

1/di = 4.2

di = 1/4.2

di = 0.238 m

Therefore, the lens should be placed 0.238 m from the screen to produce a sharp image.

I hope this helps and good luck on your test tomorrow! Remember to always double check your calculations and units to ensure accuracy.