An Object Before a Concave Mirror

Q. An object is placed 10 cm in front of a concave mirror of radius of curvature 15 cm. Where is the image, in cm, measured along the incoming light from the mirror? expects -30 cm

What the draft establishes

Fills in once a draft is checked.

The web of concepts

given read from the words equation asked

The equations it used

None yet.

Check an answer

Q. An object is placed 10 cm $d_{o} = 10$ cm in front of a concave $R = - r_{size}$ mirror of radius of curvature 15 cm $r_{size} = 15$ cm. Where is the image, in cm, measured along the incoming light from the mirror?

The playground

Inputs

distance

d_{o}

10 cm

radius

r_{size}

15 cm

Outputs

where

v

The solution

Solved with SphericalMirror

Given

$d_{o} = 10$ cm
$r_{size} = 15$ cm
$R = - r_{size}$ from “concave”

Find $v$ .

Working

$d_{o} = 10$ cm $= 0.1$ m
$r_{size} = 15$ cm $= 0.15$ m
an object in front is against the light(mirror) $u = - d_{o}$
$u = - 0.1$
$u = −0.1$ m
concave $R = - r_{size}$
$R = - 0.15$
$R = −0.15$ m
focus halfway to the centre(mirror) $f = \frac{R}{2}$
$f = \frac{(−0.15)}{2}$
$f = −0.075$ m
mirror equation(mirror) $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$
$\frac{1}{v} + \frac{1}{(−0.1)} = \frac{1}{(−0.075)}$
$v = −30$ cm
$v = −0.3$ m $= −30$ cm
$v \approx −30$ cmto 2 significant figures

Conclusion

Distances in front of the mirror are negative; the image at minus thirty centimetres is real, in front of the mirror, inverted and three times the size.

The Ruby

1require_relative "../physics"23question :an_object_before_a_concave_mirror do4  kind :numerical5  describes "An object is placed %{distance} in front of a concave mirror of radius of curvature %{radius}. " \6            "%{where}, in cm, measured along the incoming light from the mirror?"7  given distance: "10 cm"8  given radius: "15 cm"9  asks where: "Where is the image"10end

1require_relative "../questions/an_object_before_a_concave_mirror"2require_relative "../science/ray_optics_and_optical_instruments/spherical_mirror"34solve :an_object_before_a_concave_mirror, using: SphericalMirror do5  objects :mirror67  take distance: mirror.distance_in_front8  take radius: mirror.size_of_the_radius910  deduce_from "concave", mirror.radius_of_curvature => -mirror.size_of_the_radius1112  where = mirror.image_distance13  answer where:, in: "cm", figures: 21415  conclusion "Distances in front of the mirror are negative; the image at minus thirty centimetres is real, " \16             "in front of the mirror, inverted and three times the size."17end

1require_relative "../solutions/an_object_before_a_concave_mirror"23play_with :an_object_before_a_concave_mirror do4  title "An Object Before a Concave Mirror"5end

The laws

quantity	written	units	within	from
radius of curvature	$R$	m	—	SphericalMirror
size of the radius	$r_{size}$	m	—	SphericalMirror
distance in front	$d_{o}$	m	—	SphericalMirror
focal length	$f$	m	—	SphericalMirror
size of the focal length	$f_{size}$	m	—	SphericalMirror
object distance	$u$	m	—	SphericalMirror
image distance	$v$	m	—	SphericalMirror
magnification	$m$	—	—	SphericalMirror
object height	$h_{o}$	m	—	SphericalMirror
image height	$h_{i}$	m	—	SphericalMirror
object distance of ground	$u_{g}$	m	—
distance in front of ground	$d_{o,g}$	m	—
object distance of mirror	$u$	m	—
distance in front of mirror	$d_{o}$	m	—
focal length of ground	$f_{g}$	m	—
radius of curvature of ground	$R_{g}$	m	—
focal length of mirror	$f$	m	—
radius of curvature of mirror	$R$	m	—
image distance of ground	$v_{g}$	m	—
image distance of mirror	$v$	m	—
magnification of ground	$m_{g}$	—	—
magnification of mirror	$m$	—	—
image height of ground	$h_{i,g}$	m	—
object height of ground	$h_{o,g}$	m	—
image height of mirror	$h_{i}$	m	—
object height of mirror	$h_{o}$	m	—
size of the radius of mirror	$r_{size}$	m	—
size of the focal length of mirror	$f_{size}$	m	—

u_{m} = - d_{o,m}

an object in front is against the light

f_{m} = \frac{R_{m}}{2}

focus halfway to the centre

\frac{1}{v_{m}} + \frac{1}{u_{m}} = \frac{1}{f_{m}}

mirror equation

m_{m} = \frac{- v_{m}}{u_{m}}

magnification of a mirror

m_{m} = \frac{h_{i,m}}{h_{o,m}}

magnification compares the heights

u_{g} = - d_{o,g}

an object in front is against the light(ground)

u = - d_{o}

an object in front is against the light(mirror)

f_{g} = \frac{R_{g}}{2}

focus halfway to the centre(ground)

f = \frac{R}{2}

focus halfway to the centre(mirror)

\frac{1}{v_{g}} + \frac{1}{u_{g}} = \frac{1}{f_{g}}

mirror equation(ground)

\frac{1}{v} + \frac{1}{u} = \frac{1}{f}

mirror equation(mirror)

m_{g} = \frac{- v_{g}}{u_{g}}

magnification of a mirror(ground)

m = \frac{- v}{u}

magnification of a mirror(mirror)

m_{g} = \frac{h_{i,g}}{h_{o,g}}

magnification compares the heights(ground)

m = \frac{h_{i}}{h_{o}}

magnification compares the heights(mirror)

R = - r_{size}

concave