Question

A concave mirror has a focal length of 5 cm. This mirror forms an image located 15 cm in front of the mirror. What is the magnification of the mirror? (Include the sign.)

Answer 1

Answer question

Answer 2

f=-5cm

v=-15cm

1/(-15)+1/u=1/-5

u=-15/2cm

m=-v/u=-15*2/15=-2

Answer 3

1/v-1/u=1/f

1/15-1/u=-1/5

1/u = 1/15+1/5

u=3.75cm

magnification = - v/u =-(15/3.75) =-4

Answer 4

By mirror formula:-
1/u + 1/v = 1/f

u = Distance of object, +ve if real, -ve if virtual.
v = Distance of image, +ve if real, -ve if virtual.
f = Focal length, +ve if concave mirror, -ve if convex mirror.

For object,
In front of mirror = real (+ve)
Behind the mirror = virtual (-ve)***
***This is the special case for object to behind the mirror, but it's not impossible.

For image,
In front of mirror = upright wrt. object = virtual (-ve)
Behind the mirror = inverted wrt. object = real (+ve)
*wrt. = with respect to

Now, come back to calculation,
1/u + 1/(-15) = 1/5
1/u = 1/5 + 1/15
1/u = 4/15
u = 3.75 cm

Question wants magnification, so by definition,
M = v/u
M = (-5)/(+3.75)
M = -1.33

Negative sign means image is inverted wrt. object and 1.33 mean image is large than object by 1.33

Answer 5

I hope you know how to use the equation:
1/u + 1/v = 1/f

u = Distance of object, +ve if real, -ve if virtual.
v = Distance of image, +ve if real, -ve if virtual.
f = Focal length, +ve if concave mirror, -ve if convex mirror.

For object,
In front of mirror = real (+ve)
Behind the mirror = virtual (-ve)***
***This is the special case for object to behind the mirror, but it's not impossible.

For image,
In front of mirror = upright wrt. object = virtual (-ve)
Behind the mirror = inverted wrt. object = real (+ve)
*wrt. = with respect to

Now, come back to calculation,

1/u + 1/(-15) = 1/5
1/u = 1/5 + 1/15
1/u = 4/15
u = + 3.75cm

Question wants magnification, so by definition,
M = v/u

M = (-15)/(+3.75)
M = -4

Negative sign means image is inverted wrt. object

thank you.

Answer 6

Given:

Focal length(f)= -5cm

Image distance(v)= -15cm

Therefore, object distance(u)= v*f/(v-f) = (-15)*(-5)/(-15)*(-5) = -75/10 = -15/2

Therefore, magnification(m)= -v/u = -(-15)/(-15/2) = -2