Question

You wish to create an image that is 10 meters from an object. This image is to be upright and half the height of the object. You wish to accomplish this using one spherical mirror.

What is the focal length of the mirror that would accomplish this?

Why is s = 10 and s'= 20? You wish to create an image that is 10 meters from an object. This image is to be upright and half the height of the object. You wish to accomplish this using one spherical mirror.

What is the focal length of the mirror that would accomplish this?

Why is s = 10 and s'= 20? @Physics

Answer 1

image by image distance from center must be proportional to object by object distance.
Also you have 1/f = 1/u + 1 / v

Answer 2

this problem involves the smart use of spherical mirror formaulas:
the formulas needed:
1/f=1/v+1/u
m(magnification)=-v/u
before jumping anywhere let us decide the mirror type
i wanta virtual errect image half of the object size(diminshed) this is possible only when i have a convex mirror

clue 1) focal length to be +ve (convex mirror)
clue 2)object kept at -ve position on left side
clue 3)image is to be +ve right side
clue 4)DISTANCE between image and object is +ve 10m
then think in physical sense
if i blindly put v+u=10 I WUD BE WRONG
as u is -ve
so i want u to be +ve meaning -u+v=10 m-----1) (this is the tricky part)

m=1/2=-v/u=image ht/object height
then u will get u=-2V
then put in eqn 1 then solve for v and u
then find focal lentgth usin
first formula
*to check:u shud get +ve focal length

Answer 3

you sure about
1/f = 1/u + 1 / v
https://www.google.com/search?rlz=1C1ASUT_enNP447NP447&aq=f&sourceid=chrome&ie=UTF-8&q=1%2Fu+-+1%2Fv+%3D+1%2Ff

Answer 4

that is lens formula the one
1/f=1/v+1/u is mirror formula

p.s: i have books all around me i refer to all these as i dont remember the right one!

Answer 5

lens formula is
1/f=1/v-1/u note 1/v coming before 1/u

Answer 6

Oo ... yeah you are right ... didn't note at all. I must be nuts.