Problem discussions
Problem discussions
A mirror (Area= A, Mass= M, perfectly reflecting) is suspended in a vertical plane by a weightless string. Light (Intensity=I) falls normally on the mirror and the mirror is deflected from the vertical by a very small angle $$\theta$$. Obtain an expression for $$\theta$$.
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Re: Problem discussions
For perfectly reflecting mirror the light pressure on it:
$$P=\frac{2I}{c}$$, where $$c$$ is the speed of light.
Hence, the force of the light on the mirror is
$$F=P \cdot A = \frac{2IA}{c}$$
For small angles $$\theta$$:
$$T \theta = F$$, where $$T$$ is the tension in the string
and
$$T = Mg$$.
From these two equations we get
$$\theta = \frac{2IA}{Mgc}$$
$$P=\frac{2I}{c}$$, where $$c$$ is the speed of light.
Hence, the force of the light on the mirror is
$$F=P \cdot A = \frac{2IA}{c}$$
For small angles $$\theta$$:
$$T \theta = F$$, where $$T$$ is the tension in the string
and
$$T = Mg$$.
From these two equations we get
$$\theta = \frac{2IA}{Mgc}$$
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- Posts: 80
- Joined: Tue Oct 12, 2010 8:00 am
Re: Problem discussions
Where did you get this problem? It doesn't look suitable for the PGRE preparation.
Re: Problem discussions
Well, i was working out on some problems from previous entrance questions (India) where I got this.physicsworks wrote:Where did you get this problem? It doesn't look suitable for the PGRE preparation.
Why are you saying it's not suitable for the PGRE questions.? Is it a silly question or some thing?
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Re: Problem discussions
I dont think you'd be expected to know that P=2I/c for the PGRE. Maybe, but I doubt it. On second thought the I/c is perfectly reasonable, it's just the constant that I don't think they'd expect you to know (though it is a perfectly clear application of newton's third law, so....)sphy wrote:Well, i was working out on some problems from previous entrance questions (India) where I got this.physicsworks wrote:Where did you get this problem? It doesn't look suitable for the PGRE preparation.
Why are you saying it's not suitable for the PGRE questions.? Is it a silly question or some thing?
Re: Problem discussions
I think it's a good question, and it's suitability for the GRE would probably depend on the multiple-choice answer selection and whether you can come up with a clever way to eliminate two or three options if you can't remember the formula.
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- Posts: 80
- Joined: Tue Oct 12, 2010 8:00 am
Re: Problem discussions
Well...sphy wrote:Well, i was working out on some problems from previous entrance questions (India) where I got this. Why are you saying it's not suitable for the PGRE questions.? Is it a silly question or some thing?
bfollinprm wrote:I dont think you'd be expected to know that P=2I/c for the PGRE. Maybe, but I doubt it
But I also partially agree with grae313. ETS can play a game called "guess dimensions, dude".