Pinhole camera question with only two known variables?

[ldesai149]

Homework Statement

True or False: If a pinhole camera casts on the screen an image of 40.0cm in size of an object situated at a distance of 40.0m from the camera, then the size of the object is 10.0m.

Homework Equations

M = hi/ho = di/do

The Attempt at a Solution

hi = 40.0cm
do = 40.0m
ho = 10.0m (?)

M = hi/ho = 0.04m
di = dohi/ho = 0.16m
M = di/do = 0.004m

I'm guessing it is FALSE because the two values for M are different but I really have no idea how to go about a question like this. Any help would be greatly appreciated! :D

 

[collinsmark]

Hello ldesai149,

Welcome to Physics Forums!

Homework Statement

True or False: If a pinhole camera casts on the screen an image of 40.0cm in size of an object situated at a distance of 40.0m from the camera, then the size of the object is 10.0m.

Homework Equations

M = hi/ho = di/do

The Attempt at a Solution

hi = 40.0cm
do = 40.0m
ho = 10.0m (?)

M = hi/ho = 0.04m
di = dohi/ho = 0.16m

There's a mistake above involving what's in red. But read below before reaching a final conclusion in your answer. You used h_o = 10 m as part of your calculations, but you shouldn't use a specific number for h_o, because you don't know for sure what the object height actually is yet.

M = di/do = 0.004m

I'm guessing it is FALSE because the two values for M are different but I really have no idea how to go about a question like this. Any help would be greatly appreciated! :D

This is a true or false question. So at the time the statement is given, you don't really know what the object height h_o is. Maybe it's 10 m if the statement is true. But maybe it's 12 m or 100 m, or some other height, if the statement is false. It's best not to use a specific value for h_o unless you can derive that value first.

Since you don't know what h_o is, is there a way to calculate it knowing only that h_i = 0.40 m, and d_o = 40 m? If, based only on that information, you can calculate h_o to be 10 m (without using "10 m" as part of your calculations), then the statement is true. If you calculate some other number or if there is simply not enough information to derive the 10 m figure, then the statement is generally false.

 

[Redbelly98]

hi/ho = di/do

Put another way, how many variables are in that equation? How many are given in the problem statement? Can this equation be solved with that information? (Hint: do not consider h_o=10.0m as given; as collinsmark said, we do not know this.)

 

[ldesai149]

Thank you! :D It was a question on an exam and I couldn't stop thinking about it..

 

[rwisz]

I would suggest that the statement is indeed false. While we have two known variables, the size of the image and the distance of the object, we do not have enough information to determine the size of the object. This is because the magnification (M) of a pinhole camera also depends on the distance of the image (di) from the pinhole. Without knowing this distance, we cannot accurately calculate the size of the object. Additionally, the equation for magnification assumes a thin lens, which may not be the case for a pinhole camera. Therefore, we cannot make a definitive conclusion about the size of the object based on the given information.