Physics, 09.06.2020 11:57, Kitty10101

The left end of a long glass rod 8.00 cm in diameter, with an index of refraction of 1.60, is ground and polished to a convex hemispherical surface with a radius of 4.00 cm. An object in the form of an arrow 1.50 mm tall, at right angles to the axis of the rod, is located on the axis 24.0 cm to the left of the vertex of the convex surface. Find the position and height of the image of the arrow formed by paraxial rays incident on the convex surface. Is the image erect or inverted?

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answered: erica11223344

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,

$\bold {\dfrac {n_1}{s} = \dfrac {n_2}{s'} = \dfrac {n_2 -n_1}{R}}$

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,

$\bold {\dfrac {1}{0.24} = \dfrac {1.6}{s'} = \dfrac {1.6 -1}{0.04}}\\\\\bold { s' = \dfrac {1.6 }{10.83}}\\\\\bold { s' =14.77\ cm}$

The magnification formula,

$\bold {m = -\dfrac {n_1s'}{n_2s} = \dfrac {y'}{y}}$

$\bold {y' = -\dfrac {n_1s'y}{n_2s}}\\\bold {\bold {y' = -\dfrac {n_1s'}{n_2s} = 0.000577\ m = 0.577\ mm }}$

So, the magnification,

$\bold {m = \dfrac {-0.577}{1.5} = -0.38 }$

Therefore, the position of the 14.77 cm, height of the image is 0.577 mm and image is inverted as magnification is negative.

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answered: ernestsbaby6181

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:

$\frac{n_1}{s}+\frac{n_2}{s'} =\frac{n_2-n_1}{R}\\\frac{1}{0.24}+\frac{1.6}{s'}=\frac{1.6-1}{0.04} \\ \frac{1.6}{s'}=15-4.17=10.83\\ s'=\frac{1.6}{10.83}=0.1477 m=14.77cm$

From the magnification formula:

$m=-\frac{n_1s'}{n_2s}=\frac{y'}{y}\\ y'=-\frac{n_1s'y}{n_2s} =-\frac{1*0.1477*0.0015}{1.6*0.24} =-0.000577m=-0.577mm$

Magnification (m) = $\frac{y'}{y}=\frac{-0.577}{1.5}=-0.38$

Since magnification is negative, it is inverted

answered: Guest

a solenoid is created by wrapping a l = 90 m long wire around a hollow tube of diameter d = 4.5 cm. the wire diameter is d = 0.9 mm. the solenoid wire is then connected to a power supply so that a current of i = 9 a flows through the wire.

randomized variablesl = 90 m

d = 4.5 cm

d = 0.9 mm

i = 9 a

write an expression for the number of turns, n, in the solenoid. you do not need to take into account the diameter of the wire in this calculation.

calculate the number of turns, n, in the solenoid.

write an expression for the length of the solenoid (l2) in terms of the diameter of the hollow tube d.

calculate the length of the solenoid (l2) in meters.

calculate the magnitude of the magnetic field at the center of the solenoid in teslas.

explanation:

answered: Guest

Full change in the electric plus system