Converging Lens Question

[pilumnus]

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"An object is 100m from a lens with a focal point of 2.4cm. The image appears:"

A. 2.4cm behind the lens
B. 2.45cm behind the lens
C. 2.4cm infront of the lens
D. 2.45cm infront of the lens

Clearly C and D are wrong. I thought the image would appear at a greater distance (B) than the focal length, but the answer is A. Anyone have an explanation?

 

[basophilic]

just look at the lens eqn ; 1/0.024 = 1/100 + 1/i --> 1/100 is negligibel compared to 1/0.024 (1/0.024 is like 1000/25 = 40 >> 1/100 = 0.01)
put another way: 0.01/40 << 0.05/2.4, so B would be much farther. this seems a good question to practice estimation

 

[scratchrice]

Instead of using math, you can really just use logic when looking at the lens/mirror formula (f= focal point, d=distance of object, and d'= distance of image):

1/f = 1/d + 1/d' -> at 100m, d >> f so 1/d can just be treated as 0 which means that 1/f = 1/d' so d'=2.4cm

 

[basophilic]

Instead of using math, you can really just use logic when looking at the lens/mirror formula (f= focal point, d=distance of object, and d'= distance of image):

1/f = 1/d + 1/d' -> at 100m, d >> f so 1/d can just be treated as 0 which means that 1/f = 1/d' so d'=2.4cm

That's pretty much what I did; I think the OP's concern lied more in rationale for choosing 2.4 over 2.45 - especially because an additional factor of 1/100 is present; even if you can see that as negligible, there's still some doubt that the 1/100 can give just enough to change answer from 2.4 to 2.45. And since we can't use calculators, we still need a way to justify seeing 1/100 as completely negligible for this problem

 

[pilumnus]

That's pretty much what I did; I think the OP's concern lied more in rationale for choosing 2.4 over 2.45 - especially because an additional factor of 1/100 is present; even if you can see that as negligible, there's still some doubt that the 1/100 can give just enough to change answer from 2.4 to 2.45. And since we can't use calculators, we still need a way to justify seeing 1/100 as completely negligible for this problem

Exactly. But both of your answers seem legit. Thanks for the help guys!