Question

An object is placed at a distance at a of 4cm infront of a convex mirror whose focal length is 5cm.where is the image formed?

Answer 1

Answer:

Focal length of the lens (f) = 5 cm. We know, convex mirror always forms the virtual, upright and diminished. Also, Object distance in the convex mirror is always negative where as Image distance and focal length are positive. so the image distance (v) =3.33cm

Answer 2

Answer:

2.22 cm behind the convex mirror

Explanation:

As per the provided information in the given question, we have :

• Object distance (u) = – 4 cm (To the left of the mirror)
• Focal length (f) = + 5cm (As it is a convex mirror)

We are asked to calculate where the image is formed.

Here, we'll be using the mirror formula to calculate the position of the image.

Mirror Formula :

$\bigstar \boxed{\rm{ \dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f} }}$

• v denotes image distance
• u denotes object distance
• f denotes focal length

Now, by using the mirror formula,

$\longrightarrow\rm { \dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f} } \\ \\ \longrightarrow\rm { \dfrac{1}{v} + \dfrac{1}{-4} = \dfrac{1}{5} } \\ \\ \longrightarrow\rm { \dfrac{1}{v} - \dfrac{1}{4} = \dfrac{1}{5} } \\ \\ \longrightarrow\rm { \dfrac{1}{v} = \dfrac{1}{5} + \dfrac{1}{4} } \\ \\ \longrightarrow\rm { \dfrac{1}{v} = \dfrac{4 + 5}{20} } \\ \\ \longrightarrow\rm { \dfrac{1}{v} = \dfrac{9}{20} } \\ \\ \longrightarrow\rm {v= \cancel{\dfrac{20}{9}} } \\ \\ \longrightarrow\underline{\boxed{\rm {v= 2.22 \; cm}} }\; \red{\bigstar}$

∴ The image is formed 2.22 cm behind the convex mirror.

★ Learn More :

• Focal length of convex mirror is positive.
• Focal length of concave mirror is negative.
• Object distance is always taken negative as it is always placed to the left side of the mirror.