A candle is placed 9 cm in front of a concave mirror with a focal length of 6 cm. How far from the mirror will the image be located?What is the magnification of this image?
Show your work

Explanation:

Given that,

An object is place 9cm in from of a concave mirror

Then, object distance is 9cm

u = 9cm

Focal length of the mirror is 6cm

Then, f = 6cm

A. We want to find image distance

Image distance v?

From mirror formula

1 / f = 1 / u + 1 / v

Where

f is focal length

u is object distance

v is image distance

1 / f = 1 / u + 1 / v

1 / 6 = 1 / 9 + 1 / v

1 / v = 1 / 6 - 1 / 9

1 / v = 1 / 18

Take reciprocal of both sides

v = 18 cm

Since the image distance is positive, then, the image is real.

B. Magnification M?

Magnification can be determined using

M = image distance / object distance

M = v / u

M = 18 / 9

M = 2

So, the image is double.

attach the statements so i can answer : )

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west