Question

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3. The image of an object placed 16 cm from a concave
mirror is formed at a distance of 24 cm from the
mirror. Calculate the possible focal lengths of the
concave mirror from this information.​

Answer 1

Explanation:

the answer is given above

Answer 2

${\mathbf {\blue{S}{\underline{\underline{olution:-}}}}}$

$\mathfrak{\underline{AnswEr:-}}$

• The possible focal lengths of the concave mirror = - 48 Cm and - 9.6 Cm

$\mathfrak{\underline{Given:-}}$

• The Object distance is - 16 Cm
• The Image distance is + 24 Cm

$\mathfrak{\underline{Need\:To\: Find:-}}$

• The possible focal lengths of the concave mirror = ?

${\mathbf {\blue{E}{\underline{\underline{xplanation:-}}}}}$

In 1st Case:

If we have imagine distance = + 24Cm

Then,

$\:\:\:\:\dag\bf{\underline \green{According\:to\: the\:mirror\:formula:-}}$

$\bigstar \: \boxed{ \sf \: \dfrac{1}{Image\: Distance} + \dfrac{1}{Object\: distance} = \dfrac{1}{Focal\: Length } }$

$\:\:\:\:\dag\bf{\underline \blue{Putting\:the\:values:-}}$

$\longrightarrow \sf {\dfrac{1}{24} + \dfrac{(-1)}{16} = \dfrac{1}{Focal\: Length} }$

$\longrightarrow \sf { 2 - \dfrac{3}{48} = \dfrac{1}{Focal\: Length} }$

$\longrightarrow \sf {\dfrac{-1}{48} = \dfrac{1}{Focal\: Length} }$

$\longrightarrow \sf { Focal\: Length = - 48cm}$

$\rule{300}{2}$

Now, In 2nd Case:

If we have imagine distance = - 24 Cm

Then,

$\:\:\:\:\dag\bf{\underline \green{According\:to\: the\:mirror\:formula:-}}$

$\bigstar \: \boxed{ \sf \: \dfrac{1}{Image\: Distance} + \dfrac{1}{Object\: distance} = \dfrac{1}{Focal\: Length } }$

$\:\:\:\:\dag\bf{\underline \blue{Putting\:the\:values:-}}$

$\longrightarrow \sf {\dfrac{-1}{24} + \dfrac{(-1)}{16} = \dfrac{1}{Focal\: Length} }$

$\longrightarrow \sf {\dfrac{1}{Focal\: Length} = \dfrac{-2 -3}{48} }$

$\longrightarrow \sf {\dfrac{ 1}{Focal\: Length} = \dfrac{-5}{48} }$

$\longrightarrow \sf { Focal\: length = \dfrac{-48}{5} }$

$\longrightarrow \sf { Focal\: Length= - 9.6cm}$

$\:\:\:\:\dag\bf{\underline{\underline \pink{Hence:-}}}$

• The possible focal lengths of the concave mirror are - 48 Cm and - 9.6 Cm.

$\rule{300}{2}$