Light reflections in concave/convex mirrors

[freepancakes]

Homework Statement

A man polishes the insided and outside of a hubcap that is a section of a sphere. When he looks into one side of the hubcap, he sees an image of his face 30cm behind the hubcap. He then turns the hubcap over and sees another image of his face 10 cm behind the hubcap.
a)How far is his face from the hubcap?
b)What is the radius of curvature of the hubcap?
c)What is the magnification for each image?
d)Are the images real or virtual?
e)Are the images upright or inverted?

Homework Equations

1/Di + 1/Do = 1/f Di= distance of image Do=distance of object f= focal point

M= Hi/Ho = -Di/Do M= magnification Hi= height of image Ho= height of object

The Attempt at a Solution

a) i believe you have to use the first equation but i am unsure of how to use the given data in it, could you possibly do... 1/-30 + 1/-10 + 2/Di = 2/f ?

b)find the focal point and double it i believe

c)use M= -Di/Do for both but i don't know the Do from part "a"

d)virtual because the image is behind the mirror

e)upright because all virtual images are upright?

-- i think i am on the right track, but not sure--

 

[rl.bhat]

Keeping Do same, write two equation for two cases. Since R is the same fore both the case, f is the same, but sign will change. From these equation you can find Do. Once you find Do, other thing are easy.

 

[nlightner]

I would like to clarify and expand upon the information provided in the homework statement. The situation described involves light reflections in concave/convex mirrors, which can be explained using the laws of reflection and the properties of spherical mirrors.

First, let's define some terms. A concave mirror is a spherical mirror with a surface that curves inward, while a convex mirror has a surface that curves outward. The center of the sphere is called the center of curvature, and the distance from the center to the mirror's surface is known as the radius of curvature.

In this scenario, the man is looking at his reflection in a section of a sphere, which is essentially a convex mirror. When he looks into one side of the hubcap, he sees an image of his face 30cm behind the hubcap. This means that the distance of the image (Di) is 30cm, and we can use the first equation you mentioned, 1/Di + 1/Do = 1/f, to find the distance of the object (Do). Rearranging the equation, we get Do = (Di*f)/(Di-f). Substituting the known values, we get Do = (30cm * f)/(30cm-f). However, we still need to find the focal point (f) to solve for Do. The focal point can be found by dividing the radius of curvature by 2, as you mentioned. So, if the radius of curvature is 60cm, the focal point would be 30cm. Substituting this value into the equation, we get Do = (30cm * 30cm)/(30cm-30cm) = 30cm. This means that the man's face is 30cm away from the hubcap when he looks into one side.

Next, the man turns the hubcap over and sees another image of his face 10cm behind the hubcap. This means that the distance of the image (Di) is now 10cm. Using the same equation, we can find the distance of the object (Do). Substituting the known values, we get Do = (10cm * 30cm)/(10cm-30cm) = -15cm. This means that the man's face is 15cm in front of the hubcap when he looks into the other side.

Now, let's answer the specific questions:

a) The man's face is 30cm