Several optics questions, need of desperate help.

[mathrocks]

Several optics questions, need desperate help.

I have some questions about optics. I've been working on these problems unfortunately over thanksgiving break and without a book (I forgot it to bring it)
So any help you guys can give me will be awesome.

1. A concave mirror has a radius of curvature of 34.0 cm. If the mirror is immersed in water (refractive index 1.33), what is its focal length?
(I thought you would just use the equation 1/(n-1*(1/radius of curvature)), that doesn't work though for some reason)

2. An object is a distance of s from the center of a silvered spherical glass Christmas tree ornament which has a diameter of d. What is the position of its image? What is the magnification of its image?

3. A spherical, concave, shaving mirror has a radius of curvature of R. What is the magnification of a person's face when it is a distance of s to the left of the vertex of the mirror? What is the distance to the image?

4.A photographic slide is to the left of a lens. The lens projects an image of the slide onto a wall which is a distance of x to the right of the slide. The image is larger than the size of the slide by a factor of n. How far is the slide from the lens? What is the focal length of the lens?

5. Where must you place an object in front of a concave mirror with radius R so that the image is erect and 2 1/2 times the size of the object? Where is the image?


Sorry if this is too many questions but I've been working on these for awhile with no sucess. Some of these are probably so easy and I'm just wasting your time with them but I'm really struggling here, I'm not too fond of optics.

 

[mathrocks]

Any help at all will be great.

 

[wais]

Thank you for reaching out for help with your optics questions. I can understand how frustrating it can be to work on problems without having access to your textbook. Let's go through each question one by one and see if we can find some solutions.

1. The equation you mentioned is correct, but you need to take into account the change in the refractive index of the medium. In this case, the focal length can be calculated using the formula f = (n/n') * (R/2), where n and n' are the refractive indices of the medium and the mirror respectively, and R is the radius of curvature. So for this question, the focal length would be (1.33/1) * (34/2) = 22.44 cm.

2. For this question, you can use the formula 1/s + 1/s' = 2/r, where s and s' are the object and image distances, and r is the radius of the mirror. The magnification can be calculated using the formula m = -s'/s.

3. The magnification for this question can be calculated using the formula m = -s/R. To find the distance to the image, you can use the formula s' = (R^2 - s^2)/2R.

4. For this question, you can use the formula x/s = n, where x is the distance between the slide and the lens, and s is the distance between the lens and the image. The focal length can be calculated using the formula 1/f = 1/s + 1/s'.

5. For this question, you can use the formula s' = -f/s, where s is the distance between the object and the mirror, and s' is the distance between the image and the mirror. The image will be located at a distance of 2.5s from the mirror.

I hope these explanations and formulas help you solve these problems. Remember, practice makes perfect, so keep working at it and don't get discouraged. Good luck!