physics question (plane mirror)

[theonlytycrane]

1. A far-sighted person can see objects clearly no closer than 300 cm away. What is the minimum distance from a plane mirror such a person must be to see his reflection clearly.

a) 75 cm
b) 150 cm
c) 300 cm
d) 600 cm

The answer given is (b). Light from the person reflects off of the mirror back to the person. That light ray from the mirror to the person is only 150 cm away, so wouldn't it be blurry? I didn't think it mattered that the original light ray "traveled" 300 cm.

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[betterfuture]

The person can see no less than 300cm because he is farsighted. When you stand in front of a mirror, you see a reflection of yourself at the same distance behind the mirror. So if you stand 150cm in front of the mirror, you would see a reflection of yourself 150cm behind the mirror. 150+150=300cm. Hope that made sense.

 

[theonlytycrane]

That makes sense in terms of math, but I'm conflicted because the image behind the mirror doesn't actually emit any light. Is the plane mirror tricking my brain into thinking it is and since that distance is 300 cm I can now see it?

 

[aldol16]

That makes sense in terms of math, but I'm conflicted because the image behind the mirror doesn't actually emit any light. Is the plane mirror tricking my brain into thinking it is and since that distance is 300 cm I can now see it?

Your eyes are presumably lacking in detecting where the image is, not where the light emitted comes from.

 

[aalamruad]

1. A far-sighted person can see objects clearly no closer than 300 cm away. What is the minimum distance from a plane mirror such a person must be to see his reflection clearly.

a) 75 cm
b) 150 cm
c) 300 cm
d) 600 cm

The answer given is (b). Light from the person reflects off of the mirror back to the person. That light ray from the mirror to the person is only 150 cm away, so wouldn't it be blurry? I didn't think it mattered that the original light ray "traveled" 300 cm.

I think it'll help you to understand the cause of farsightedness. Basically, the lenses in the person's eyes can't quite converge the incoming light enough to focus it properly. Light rays emitted from a point that's far away are closer to parallel than objects up close, so they don't need to be refracted as much to be focused, which is why farsighted people can see objects that are far away. Conversely, close objects have light rays that diverge at a wider angle when hitting the person's lenses, meaning that they need to be refracted more to be in focus, which their lenses can't quite do. Thus, the only thing that really matters in terms of the minimum distance at which a farsighted person can clearly see an object is how close the light rays are to parallel. Light that travels farther distances is closer to parallel/has a smaller angle of divergence/doesn't need to be refracted as much. In the problem with the plane mirror, the light hitting the farsighted person's eyes has indeed traveled 300 cm when s/he is standing 150 cm from the mirror, because those light rays had to travel 150 cm from the person to the mirror, and then 150 cm from the mirror to the person's lenses. This means that the light rays hitting their eyes will be exactly as far from parallel as an object that they're looking at that's 300 cm away.

Hope that wasn't too confusing - did that make sense?

 

[BerkReviewTeach]

I have to say how inspired I am by this thread. SDN, like everything in life, follows a sine wave of varying amplitude. I had been disappointed in some of the posts over the past year in terms of tone and quality. Lately though, there have been some really excellent and well-reasoned posts by people passionate about the material and wanting to help others. All four of you in this thread have been a big part of that resurgence and you epitomize the spirit that has kept SDN strong for the years that I have been posting.

Thank you for caring to post intelligent, helpful, and friendly answers. You are awesome!