Question

A concave lens of Focal length 15cm forms an image 10cm from the lens. how far is the object from the lens ? ​

Answer 1

$\huge {\orange {\bf {\underline {\underline {ÀnSwer}}}:-}}$

The object is placed at a distance of 30cm from the concave lens .

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Explaination :-

⟶ Gíven :-

• Image distance, v = -10cm
• Focal length, f = -15cm

⟶ To fínd :-

object distance

⟶ Solutíon :-

Using lens formula,

.i.e.,

$\hookrightarrow \bold {\sf \frac{1}{v} - \frac{1}{u} = \frac{1}{f} } \\ \\ \hookrightarrow \: \sf \frac{1}{ - 10} - \frac{1}{u} = \frac{1}{ - 15} \\ \\ \hookrightarrow \: \sf - \frac{1}{u} = - \frac{1}{15} + \frac{1}{10} \\ \\ \hookrightarrow \: \sf - \frac{1}{u} = \frac{ - 2 + 3}{30} \\ \\ \hookrightarrow \: \sf - \frac{1}{u} = \frac{1}{30} \\ \\ \hookrightarrow \boxed{ \bf u = - 30cm}$

Thus, the object is placed at a distance of 30cm from the concave lens

[Note :- The minus sign with object distance shows that the object is on its left side]

Answer 2

Answer :

➥ The object distance from the lens = 30 cm

Given :

➤ Image Distance from lens = -10 cm

➤ Focal length from lens = -15 cm

To Find :

➤ Object distance from lens = ?

Required Solution :

We can find object distance from lens by using the lens formula which says:

† 1/v - 1/u = 1/f †

Here,

• v is the Image distance from lens.
• u is the Object distance from lens.
• f is the focal length from lens.

So let's find Object distance (u) !

From lens formula

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

$\tt{:\implies \dfrac{1}{ - 10} - \dfrac{1}{u} = \dfrac{1}{ - 15} }$

$\tt{:\implies - \dfrac{1}{u} = -\dfrac{1}{15} + \dfrac{1}{10} }$

$\tt{:\implies - \dfrac{1}{u} = \dfrac{ - 2 + 3}{30} }$

$\tt{:\implies - \dfrac{1}{u} = \dfrac{1}{30} }$

$\bf{:\implies \underline{ \: \: \underline{ \red{ \: \: u = - 30 \: cm \: \: }} \: \: }}$

【NOTE : The minus shows that the object is on the left side of the lens.】

║Hence, the object should be placed at a distance of 30 cm in front of the concave lens.║