Limiting angle of resolution question

[glid02]

I have a question about a limiting angle of resolution when viewed from a circular aperture.

I'm trying to find the distance between two lights of a certain wavelength. The lights appear to merge into one at a given distance when viewed through an aperture of some given size.

So far I've tried these equations:
theta(min)=1.22(lambda/D)

I know both lambda and D (diameter), so I now know theta(min).

Now I've tried
theta(min)=d/L

where I know L(distance at which the lights appear to merge) but not d. After solving for d I still can't get the right answer. If anyone could help me out a it'd be great. Thanks a lot.

 

[Chi Meson]

It looks like you did the right thing. Give us the values and we'll check your math.

The formulas you used are for "small angle approximations." If L is not very large, then the answer will be off.

 

[Andrew Mason]

I have a question about a limiting angle of resolution when viewed from a circular aperture.

I'm trying to find the distance between two lights of a certain wavelength. The lights appear to merge into one at a given distance when viewed through an aperture of some given size.

So far I've tried these equations:
theta(min)=1.22(lambda/D)

I know both lambda and D (diameter), so I now know theta(min).

Now I've tried
theta(min)=d/L

where I know L(distance at which the lights appear to merge) but not d. After solving for d I still can't get the right answer. If anyone could help me out a it'd be great. Thanks a lot.

Try $sin\theta_{min} = d/L$

AM

 

[glid02]

A child is standing at the edge of a straight highway watching her grandparents' car driving away at 20.6 m/s. The air is perfectly clear and steady, and after 13.1 min the car's two taillights (645 nm) appear to merge into one. Assuming the diameter of the child's pupils is 4.97 mm, calculate the width of the car.

That's the question, I have 2.564 m as the answer.

 

[Andrew Mason]

A child is standing at the edge of a straight highway watching her grandparents' car driving away at 20.6 m/s. The air is perfectly clear and steady, and after 13.1 min the car's two taillights (645 nm) appear to merge into one. Assuming the diameter of the child's pupils is 4.97 mm, calculate the width of the car.

That's the question, I have 2.564 m as the answer.

You have everything you need. Use $\theta = d/L$ and [tex]\theta = 1.22\lambda/D[/itex] where D is the diameter of the pupil, L is the distance of the car and d is the width of the car.

What are you using for L? How do you calculate it? That is probably where your problem is. The answer 2.56 m is correct using the information provided.

AM