Respuesta :
Answer:
s' = 14.77 cm
height of image = 0.577 mm
Since magnification is negative, it is inverted
Explanation:
Where
index of refraction (n₁) = 1 for air,
index of refraction for glass (n₂) = 1.60,
object distance from vertex to spherical surface (s) = 24 cm = 0.24 m,
radius (R) is positive since it is in the same direction as the refracted light = 4 cm = 0.04 m
image distance from vertex to spherical surface (s')
Height of image = y'
height of object = y = 1.5 mm = 0.0015 m
Object - image formula for spherical reflecting surface is:
[tex]\frac{n_1}{s}+\frac{n_2}{s'} =\frac{n_2-n_1}{R}\\\frac{1}{0.24}+\frac{1.6}{s'}=\frac{1.6-1}{0.04} \\ \frac{1.6}{s'}=15-4.17=10.83\\ s'=\frac{1.6}{10.83}=0.1477 m=14.77cm[/tex]
From the magnification formula:
[tex]m=-\frac{n_1s'}{n_2s}=\frac{y'}{y}\\ y'=-\frac{n_1s'y}{n_2s} =-\frac{1*0.1477*0.0015}{1.6*0.24} =-0.000577m=-0.577mm[/tex]
Magnification (m) = [tex]\frac{y'}{y}=\frac{-0.577}{1.5}=-0.38[/tex]
Since magnification is negative, it is inverted
The position of the 14.77 cm, height of the image is 0.577 mm and image is inverted as magnification is negative.
The formula of image formation by spherical reflecting surface,
[tex]\bold {\dfrac {n_1}{s} = \dfrac {n_2}{s'} = \dfrac {n_2 -n_1}{R}}[/tex]
Where,
n1 - index of refraction for air = 1
n2 - index of refraction for glass = 1.60,
s - object distance from vertex to spherical surface = 24 cm = 0.24 m
R - radius = 4 cm = 0.04 m
Put the values in the formula,
[tex]\bold {\dfrac {1}{0.24} = \dfrac {1.6}{s'} = \dfrac {1.6 -1}{0.04}}\\\\\bold { s' = \dfrac {1.6 }{10.83}}\\\\\bold { s' =14.77\ cm}[/tex]
The magnification formula,
[tex]\bold {m = -\dfrac {n_1s'}{n_2s} = \dfrac {y'}{y}}[/tex]
[tex]\bold {y' = -\dfrac {n_1s'y}{n_2s}}\\\bold {\bold {y' = -\dfrac {n_1s'}{n_2s} = 0.000577\ m = 0.577\ mm }}[/tex]
So, the magnification,
[tex]\bold {m = \dfrac {-0.577}{1.5} = -0.38 }[/tex]
Therefore, the position of the 14.77 cm, height of the image is 0.577 mm and image is inverted as magnification is negative.
To know more about magnification,
https://brainly.com/question/21370207
