Derive 1 f = 1 v + 1 u formula for spherical mirrors.

From the given figure, we notice that △ A B O and △ A ’ B ’ O are similar. Therefore, A ′ B ′ / A B = O B ′ / O B (equation one) Similarly, △ A ’ B ’ F and △ O C F are similar, hence A ′ B ′ / O C = F B ′ / O F But, O C = A B Hence, A ' B ' / A B = F B ' / O F (equation two) Equating equations (1) and (2), we get O B ′ / O B = F B ′ / O F = ( O B ′ − O F ) / O F Substituting the sign convention, we get O B = - u , O B ’ = v a n d O F = f v / − u = ( v − f ) / f v f = − u v + u f o r u v = u f − v f Dividing both the sides by u v f , we get ⇒ 1 / f = 1 / v − 1 / u The above equation is known as the Lens formula. It relates the focal length of a lens with the distance of an object which is placed in front of it and the image formed of that object.

Derive 1 f = 1 v + 1 u formula for spherical mirrors.

From the given figure, we notice that △ A B O and △ A ’ B ’ O are similar. Therefore, A ′ B ′ / A B = O B ′ / O B (equation one) Similarly, △ A ’ B ’ F and △ O C F are similar, hence A ′ B ′ / O C = F B ′ / O F But, O C = A B Hence, A ' B ' / A B = F B ' / O F (equation two) Equating equations (1) and (2), we get O B ′ / O B = F B ′ / O F = ( O B ′ − O F ) / O F Substituting the sign convention, we get O B = - u , O B ’ = v a n d O F = f v / − u = ( v − f ) / f v f = − u v + u f o r u v = u f − v f Dividing both the sides by u v f , we get ⇒ 1 / f = 1 / v − 1 / u The above equation is known as the Lens formula. It relates the focal length of a lens with the distance of an object which is placed in front of it and the image formed of that object.

Name the type of mirror used in side / rearview mirror of a vehicle. Support your answer with reason.

A convex mirror is used in the side/rearview mirror of a vehicle. It always provides an erect image and has a larger field of view as they are curved outwards. A convex mirror is used as side rearview mirror, because its field of view is larger, and it forms virtual, erect and diminished images of objects behind.

E M B I B E

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR SCIENCE>Chapter 10 - Light - Reflection and Refraction>Gujarat Board-2020>Q 12

MEDIUM

10th Gujarat Board

IMPORTANT

Earn 100

Draw the diagram of image formation by a concave mirror when the object is placed between centre of curvature and focus of the concave. Also state the position, size and nature of the image formed.

Important Questions on Light - Reflection and Refraction

EASY

10th Gujarat Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR SCIENCE>Chapter 10 - Light - Reflection and Refraction>Gujarat Board-2019>Q 4

The optical fibre used in signal communication works on which principle?

EASY

10th Gujarat Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR SCIENCE>Chapter 10 - Light - Reflection and Refraction>Gujarat Board-2019>Q 6

"Ray of light travels from optically rarer medium to optically denser medium, it moves towards normal and when it travels from optically denser to optically rarer medium it moves away from the normal is known as refraction of light". Which of the following pentagon figures shows the correct refraction of light.

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