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Answers
Answer:
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Step-by-step explanation:
Answer:
The image as for behind the mirror as the object is in front of the mirror.
Step-by-step explanation:
Given : An object OA placed at a point A, LM be a plane mirror, D be an observer and OB is the image.
To prove :The image is as far behind the mirror as the object is in front of the mirror i.e.,
OB=OA
Proof : ∴CN⊥ and AB⊥LM
⇒ AB∣∣CN
∠A=∠i [alternate interior angles]...(i)
∠B=∠r [corresponding angles]...(ii)
Also ∠i=∠r [∵incident angle = reflected angle]...(iii)
From Eqs. (i), (ii) and (iii), ∠A=∠B
In ΔCOB and ΔCOA, ∠B=∠A [Proved above]
∠1=∠2 [each90∘]
and CO=CO[common side]
∴ ΔCOB≅ΔOAC [by AAS congruence rule]
⇒ OB=OA [by CPCT]
Alternate Method
InΔOBC and ΔOAC, ∠1=∠2 [each 90∘]
Also, ∠i=∠r [∵ incident angle =redlected angle]...(i)
On multiplying both sides of Eq. (i) by - 1 and than adding 90∘ both sides, we get
90∘−∠i=90∘−∠r
⇒ ∠ACO=∠BCO
and OC=OC[Commonside]
∴ ΔOBC≅ΔOAC [by ASA conguence rule]
⇒ OB=OA [by CPCT]
Hence, the image as for behind the mirror as the object is in front of the mirror.