Question

an object of height 2 cm is placed at 20 cm distance in front of a concave mirror whose focal length is 15 cm calculate height of the image​

Answer 1

Answer:

$\boxed{\mathfrak{Height \ of \ the \ image \ (h_i) = -6 \ cm}}$

Given:

Object height ($\sf h_o$) = 2 cm

Image distance (u) = -20 cm

Focal length (f) = -15 cm

Explanation:

Lateral magnification of spherical mirror:

$\boxed{ \bold{m = \dfrac{h_i}{h_o} = \dfrac{f}{f-u}}}$

$\sf h_o \longrightarrow$ Image height

By substituting values in the formula we get:

$\rm \implies \dfrac{h_i}{2} = \dfrac{ - 15}{ - 15-( - 20)} \\ \\ \rm \implies \dfrac{h_i}{2} = \dfrac{ - 15}{ - 15 + 20} \\ \\ \rm \implies \dfrac{h_i}{2} = \dfrac{ - 15}{ 5} \\ \\ \rm \implies \dfrac{h_i}{2} = - 3 \\ \\ \rm \implies h_i = - 3 \times 2 \\ \\ \rm \implies h_i = - 6 \ cm$

Note: Negative sign in the image height denotes that the image formed is inverted.

Answer 2

Answer :

➥ Height of the image = -6 cm

Given :

➤ Distance of image (u) = - 20 cm

➤ Focal length of the mirror (f) = - 15 cm

To Find :

➤ Height of the image (h₂) = ?

Required Solution :

To find the height of the image, at first we need to find the distance of image from mirror, after that we will find Height of the image.

We can find distance of the image by using the mirror formula which says:

★ 1/v + 1/u = 1/f ★

Here,

• v is the distance of image from mirror.
• u is the distance if the object from mirror.
• f is the focal length of the mirror.

✎ So let's calculate Distance of image (v) !

$\tt{: \implies \dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f} }$

$\tt{: \implies \dfrac{1}{v} + \dfrac{1}{ - 20} = \dfrac{1}{ - 15} }$

$\tt{: \implies \dfrac{1}{v} - \dfrac{1}{ 20} = - \dfrac{1}{15} }$

$\tt{: \implies \dfrac{1}{v} = - \dfrac{1}{15} + \dfrac{1}{20}}$

$\tt{: \implies \dfrac{1}{v} = \dfrac{ - 4 + 3}{60} }$

$\tt{: \implies \dfrac{1}{v} = \dfrac{4 - 3}{60} }$

$\tt{: \implies \dfrac{1}{v} = - \dfrac{1}{60} }$

$\bf{: \implies \underline{ \: \: \underline{ \orange{ \: \: v = - 60 \: cm\: \: }} \: \: }}$

【NOTE : The minus sign shows the left side of mirror.】

Now, we have Height of the object, distance of the image and distance of the object,

• Height of the object (h₁) = 2 cm
• Distance of the image (v) = -60 cm
• Distance of the object (u) = -20 cm

And we need to find Height of the image (h₂)

We can find Height of the image by using the formula which syas:

★ h₂/h₁ = -v/u ★

Here,

• h₂ is the Height of the image.
• h₁ is the Height of the object.
• v is the Distance of the image.
• u is the Distance of the object.

✎ So let's find Height of the image (h₂) !

$\tt{: \implies \dfrac{h_2}{h_1} = - \dfrac{v}{u} }$

$\tt{: \implies \dfrac{h_2}{2} = - \dfrac{ \cancel{ - }60}{ \cancel{ -} 20}}$

$\tt{: \implies \dfrac{h_2}{2} = -\dfrac{6\cancel{0}}{2\cancel{0}}}$

$\tt{: \implies \dfrac{h_2}{2} = - \cancel{\dfrac{6}{2}}}$

$\tt{: \implies \dfrac{h_2}{2} = - 3}$

$\tt{: \implies h_2 = - 3 \times 2}$

$\bf{: \implies \underline{ \: \: \underline{ \red{ \: \: h_2 = -6 \: cm \: \: }} \: \: }}$

【NOTE : The minus sign here show that the image is formed below the principal axis. That is, real and inverted image.】

║Hence, the Height of the image is -6 cm.║