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A 10 cm long pencil is placed 5 cm in front of a concave mirror having a radius of curvature of 40 cm.

(i) Determine the position of the image formed by this mirror.

(ii) What is the size of the image?

(iii) Draw a ray diagram to show the formation of the image as mentioned in the part (i).

Reflection of Light

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Answer

(i) Given,

Object distance (u) = -5 cm

Radius of curvature (r) = 40 cm

Image distance (v) = ?

Focal length (f) = r2\dfrac{r}{2} = 402\dfrac{40}{2} = -20 cm [f in case of a concave mirror is negative.]

Using formula,

1f\dfrac{1}{\text{f}} = 1v\dfrac{1}{\text{v}} - 1u\dfrac{1}{\text{u}}

We get,

-120\dfrac{1}{\text{20}} = 1v\dfrac{1}{\text{v}} - 15\dfrac{1}{\text{5}}

1v\dfrac{1}{\text{v}} = -120\dfrac{1}{\text{20}} + 15\dfrac{1}{\text{5}}

1v\dfrac{1}{\text{v}} = −1+420\dfrac{-1+4}{\text{20}} = 320\dfrac{3}{20}

So, v = 203\dfrac{20}{3} = 6.67 cm

Hence, image is obtained at 6.67 cm behind the mirror.

(ii) Size of object (ho) = 10 cm

Size of the image (hi)= ?

From formula,

m = hiho\dfrac{hi}{ho} = - vu\dfrac{\text{v}}{\text{u}}

Substituting we get,

hi10\dfrac{h_i}{10} = −6.67−5-\dfrac{6.67}{-5}

hi = 10 x 6.675\dfrac{6.67}{5} = 13.34 cm

Hence, size of image is 13.34 cm

(iii) Ray diagram showing the formation of the image is given below:

A 10 cm long pencil is placed 5 cm in front of a concave mirror having a radius of curvature of 40 cm. (i) Determine the position of the image formed by this mirror. (ii) What is the size of the image? (iii) Draw a ray diagram to show the formation of the image as mentioned in the part (i). CBSE 2024 Science Class 10 Sample Question Paper Solved.

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