How can I solve these mirror problems without getting the wrong answer?

[Kawrae]

This is driving me crazy I am ready to either bash my head through a window or kill something. I can't get any of these homework problems and I have no idea why... These are webassign problems so it tells me if its the wrong answer but naturally doesn't tell me what I'm doing wrong... so I am just going to post them all under one thread, here goes

1. A person walks into a room with two flat mirrors on opposite walls, which produce multiple images. When the person is 5.00 ft from the mirror on the left wall and 12.0 ft from the mirror on the right wall, find the distance from the person to the first three images seen in the mirror on the left.
distance to first image:
distance to second image:
distance to third image:

>>> I had the distance to the first image as 5.00 feet. Because I thought the distance an object is from a mirror will equal how far the image is from the mirror. And then I had the second image as being 29 feet away... I have NO idea why this isn't right. Or how to solve it at all.

2. A concave mirror has a focal length of 40.0 cm. Determine the object position for which the resulting image is upright and four times the size of the object.

>> I think I might be on the right track but am just having trouble with the math. I know that 1/p = 1/f - 1/q and I also know that M=-q/p ... but I don't know q and am having a real hard time trying to figure it out without it. How can I solve it?!

3. An object is 12.0 cm from the surface of a reflective spherical Christmas-tree ornament 7.00 cm in diameter. (Use the correct sign conventions for your answers.)
What is the magnification?
What is the image distance?

>> I said R = 3.5, because it is half of the diameter. Then I said f=R/2=-1.75 because f is behind the mirror. Then I tried just plugging into 1/q=1/f - 1/p to get the image distance and I got -1.17. Which is wrong. And I don't understand why. AAAARGHHHHHHHH
If I had q I could find the magnification by using M=-q/p

4. A goldfish is swimming inside a spherical plastic bowl of water, with index of refraction 1.33. If the goldfish is 11.5 cm from the wall of the 16.0 cm radius bowl, where does it appear to an observer outside the bowl?

>> I tried using the equation n1/p + n2/q = n2-n1/R and had n1 = 1.00 (air) and n2 = 1.33 (water). R I said was -16.0 and p = 11.5. I plugged everything in and got q being -12.4. What am I doing wrong? How can I solve this??

Please help me! I don't understand what I am doing wrong?!

 

[ehild]

1. I had the distance to the first image as 5.00 feet. Because I thought the distance an object is from a mirror will equal how far the image is from the mirror. And then I had the second image as being 29 feet away... I have NO idea why this isn't right.

29 feet away from the MIRROR. And it was asked from the person.

2. A concave mirror has a focal length of 40.0 cm. Determine the object position for which the resulting image is upright and four times the size of the object.

>> I think I might be on the right track but am just having trouble with the math. I know that 1/p = 1/f - 1/q and I also know that M=-q/p ... but I don't know q

M is given, M=4, so q= -4p.

3.

>> I said R = 3.5, because it is half of the diameter. Then I said f=R/2=-1.75 because f is behind the mirror. Then I tried just plugging into 1/q=1/f - 1/p to get the image distance and I got -1.17. Which is wrong.

You've just miscalculated something. Try again.

4. A goldfish is swimming inside a spherical plastic bowl of water, with index of refraction 1.33. If the goldfish is 11.5 cm from the wall of the 16.0 cm radius bowl, where does it appear to an observer outside the bowl?

>> I tried using the equation n1/p + n2/q = n2-n1/R and had n1 = 1.00 (air) and n2 = 1.33 (water). R I said was -16.0 and p = 11.5. I plugged everything in and got q being -12.4. What am I doing wrong? How can I solve this??

If you consider air the first medium and water the second one then your object is behind the surface so its distance is negative. On the other hand, r is positive as the bowl looks convex from outside.

 

[einstone]

Answer to Q.1: The distance to image #2=34ft (= 29+5. This image is the reflection of the first image in the mirror on the right in the other mirror). The next image to the right is the reflection of the first image on the left(22ft 'behind' the right mirror). Reflect this image in the mirror on the left & you'll get the next answer(= 44ft?).
Q.2,3,4 -- Bogged down by the Cartesian sign convention?! You seem to know how to solve the problems. Just have a good look at the formulae & conventions (& don't bash your head or kill anything! A year ago, these formulae swamped me 10 times more than they are swamping you!).
Regards,
Einstone.

 

[Kawrae]

>> I said R = 3.5, because it is half of the diameter. Then I said f=R/2=-1.75 because f is behind the mirror. Then I tried just plugging into 1/q=1/f - 1/p to get the image distance and I got -1.17. Which is wrong.



You've just miscalculated something. Try again.

I went back through and tried this again and got the same thing? I don't understand what I'm doing wrong... I'm using f as negative because its inside the ball and behind the mirror. And R as positive... can someone explain how to do this problem using very small words?

 

[ehild]

I went back through and tried this again and got the same thing? I don't understand what I'm doing wrong... I'm using f as negative because its inside the ball and behind the mirror. And R as positive... can someone explain how to do this problem using very small words?

f is negative, that is correct.

1/p + 1/q = 1/f, 1/p = -1/1.75 -1/12 = -0.6548 --->p = - 1.53.

ehild

 

[Kawrae]

Thank you very much! I was using -1/1.75-1/3.5... I see what I did wrong now. Ack too many variables thanks!