Question

2.0 centimetre object is placed to perpendicular to the principal axis of a convex lens of focal length 10cm the distance of the object from the lens is 15 cm find the nature position and size of the image also find its magnification​

Answer 1

$\implies\texttt\green{Refer \: to \: the \: attachment}$

Answer 2

$\boxed{\bf{ \blue{\bigstar Find \longrightarrow }}}$

• Image distance ( v) = ?
• Image size (h$_i$) = ?
• Nature of image?

$\boxed{\bf{ \orange{\bigstar Given \longrightarrow }}}$

• size of object (h$_o$) = 2.0 cm
• Focal length of convex lens (f) = 10 cm
• Object distance from the lens (u) = -15 cm

$\boxed{\bf{ \purple{\bigstar Formulas \ used \longrightarrow }}}$

• $\bf{\dfrac{1}{v} - \dfrac{1}{u}= \dfrac{1}{f}}$
• $\sf{ (m) = \dfrac{h_i} { h_o} = \dfrac{v}{u} }$

where, v= image distance,

u= object distance,

f= focal length,

m= magnification,

hi= height of image,

ho= height of object.

$\boxed{\bf{ \green{\bigstar SoLution \longrightarrow }}}$

we know the formula of mirror,

$\bf{\dfrac{1}{v} - \dfrac{1}{u}= \dfrac{1}{f}}$

$\bf{\dfrac{1}{v} = \dfrac{1}{f} + \dfrac{1}{u}}$

put values in this we get,

$\bf{\dfrac{1}{v} = \dfrac{1}{10} - \dfrac{1}{15}}$

$\bf{\dfrac{1}{v} = \dfrac{1}{30}}$

Thus, v = 30 cm

now we will find the size of image,

we know the formula of Linear magnification , i.e

$\sf{ (m) = \dfrac{h_i} { h_o} = \dfrac{v}{u} }$

put given values in the formula we get,

$\bf{\dfrac{h_i}{2} = \dfrac{30}{-15}}$

$\bf{ h_i \times -15 = 30\times 2}$

$\bf{h_i = \dfrac{60}{ -15} }$

$\bf{h_i = -4 cm}$

hence,

Image distance = 30cm

Size of image = -4cm

Nature of image = REAL and INVERTED.

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For the attachment here is solution->

$\boxed{\bf{ \red{\bigstar Question \longrightarrow }}}$

Light enters from air to glass having refractive index 1.50. What is the speed of light in the glass? The speed of light in vacuum is 3 x 10⁸ ms-1.

$\boxed{\bf{ \orange{\bigstar Given \longrightarrow }}}$

• Speed of light in vacuum (c) = 3 × 108 ms-1
• Refractive index of glass (ng) = 1.50

$\boxed{\bf{ \pink{\bigstar SoLution \longrightarrow }}}$

$\sf{Refractive\ index\ of\ a\ medium = \dfrac{Speed\ of\ light\ in\ vacuum}{Speed\ of\ light\ in\ the\ medium}}$

$\sf{Refractive\ index\ of\ glass = \dfrac{Speed\ of\ light\ in\ vacuum}{Speed\ of\ light\ in\ the\ glass}}$

$\sf{Speed\ of\ light\ in\ the\ glass\ (v) = \dfrac{Speed\ of\ light\ in\ vacuum}{Refractive\ index\ of\ glass}}$

put values we get,

$\sf{v = \dfrac{c}{ng} }$

$\sf{v = \dfrac{(3 \times 108)}{1.50} }$

$\bf{v = 2 \times 10^8 m/s}$

hence, the speed of light in the glass is 2×10⁸m/s.

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