Question

Use Polya method to solve the problem. Prep, Plan, execute, check. Please do not respond to the question if you are not planning on using this method so i can see what you're doing.

An object 10.0 cm tall is placed at the zero mark of a meterstick. A spherical mirror located at some point on the meterstick creates an image of the object that is upright, 4.00 cm tall, and located at the 42.0-cm mark of the meterstick. (a) Is the mirror convex or concave? (b) Where is the mirror? (c) What is the mirror’s focal length?

Use Polya method to solve the problem. Prep, Plan, execute, check. Please do not respond to the question if you are not planning on using this method so i can see what you're doing.

polya method is used to explain how you answer a question. it is done in four steps.

1 prep- include variables an pictures and equations you will use

2. plan- plan what you will fo and how you will use equation

3. execute- solve the problem

4. check- use unit check and going backward such as solving for a variable that is known with the answer found.

Answer 1

Prep -

The given data is

height of the image, hi = 4 cm

height of image, ho = 10 cm

since the image is upright and smaller than the object, it has to be the convex mirror

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plan -

Our first aim is to solve for position of mirror. Note that position of mirror is also called as object distance relative to object.

We can assume position of the mirror as 'x' then we can solve for object distance and image distance where are given total distance as 42 cm. We will then use the magnification equation to form another equation in terms of p and q.

then we will simply use mirror/lens equation to find the focal length.

+ focal length = concave mirror

- focal length = convex mirror

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execute

Ok, Let's call mirror position as 'x'

this means object distance, p = x -------- (1)

and

q = x - 42 ------------ (2)

we also know that

magnification, m = -q / p = hi / ho

so,

-q/p = 4 / 10

-q/p = 0.4

q = - 0.4 p --------- (3)

combining (1) , (2) and (3), we have

x - 42 = - 0.4 x

- 42 = - 0.4 x - x

42 = 1.4 x

x = 42 / 1.4

x = 30 cm ( This is the position of mirror)

and

Now,

to find mirror's focal length

1/f = 1/p + 1/q

where p = 30 cm

q = 30 - 42 = - 12 cm

so,

1/f = 1/30 - 1/12

1/f = - 0.05

f = -20 cm

As the focal length is negative, the mirror is a convex mirror !!!

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Check

we can use the focal length to find the magnification. Suppose we don't know image distance (q)

then

1/q = 1/f - 1/p

1/q = - 1/20 - 1/30

1/q = - 0.08333

q = -12 cm

and

magnification = -q / p = - ( -12) / 30

m = 0.4

as m is positive, image is upright and as m < 1, image is smaller than the object !!!