Some problems from geometric optics

Q1) Two mirrors are inclined at an angle \(\alpha\).Light ray is inclined parallel to one og the mirrors.The ray will start retracing its path after **third reflection** if \(\alpha=\) .The figure is above

Q2) A point object is kept in front of a plane mirror. The plane mirror is doing SHM of **amplitude** \(2~ cm\).The plane mirror moves along the \(x-axis\) and \(x-axis\) is normal to the mirror.The amplitude of the mirror is such that the object is always in front of mirror.The amplitude of SHM of the image is

Q3) A person's eye is at height of \(1.5~m\). He stands in front of a \(0.3~m\) long plane mirror which is \(0.8~m\) above the ground. the length of the image he sees of himself is

Q4) A person is standing in a room of width \(200~cm\). A plane mirror of **vertical** length \(10~cm\) is fixed on a wall in front og the person. The person looks into the mirror from distance \(50~cm\).How much width of the wall behind him will he able to see (assume that he uses the full mirror).

Q5) An unnumbered wall clock shows time \(04:25:37\), where \(1st\) terms represent hours,\(2nd\) represent minutes and \(3rd\) represents seconds. What time will its image in a plane mirror show..

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For problem 1 and 2 check the first image, I'll explain problem 3(answer for 1 is 30 degrees)

At first and a ray from A to top end of mirror after reflection it will hit C(C will be at distance .8m from A), Now similarly send a ray to bottom end, after reflection it will hit E(E is at a distance 1.4m from A) and he can see himself from C to E which equals 0.6m.

Similarly in problem 4 send ray to ends of mirror and apply simple geometr(our answer = 2x + 10 = 50)

For problem 5 answer is equivalent when you put mirror on axis containing numbers 6 and 12.

Pro tip: In mostly all plane mirror problems you just need to send rays at extremities of mirror and apply simple geometry. – Krishna Sharma · 2 years, 2 months ago

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Did you have doubts in these questions or did you want to test us ? I am just curious ! – Azhaghu Roopesh M · 2 years, 2 months ago

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– Rohit Shah · 2 years, 2 months ago

He would have posted it as a question to test usLog in to reply

I wanted to ask you this , what does your profile pic depict ? I can only guess that it's a fabric of some sort , which has been hand stitched, as evident from the fact that you have used it a a profile pic , by you (perhaps) ,and the lines aren't quite straight so I'm guessing you are inexperienced at it .

Please tell me I am wrong !

Btw I did it just for fun :) – Azhaghu Roopesh M · 2 years, 2 months ago

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– Rohit Shah · 2 years, 2 months ago

That is a fabric rather a sofa cover which I had uploaded initially. But then I didn't change it later. I agree that its absolutely meaningless.Log in to reply

Here I thought that you had posted a piece of your work . That's why I don't make these guesses online . – Azhaghu Roopesh M · 2 years, 2 months ago

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1) 30 2) 4 cm 3) 0.6 m 4) 50 cm 5) 7:34:23 – Rohit Shah · 2 years, 2 months ago

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– Tanishq Varshney · 2 years, 2 months ago

1) 30 degrees and 5) 7:34:23.Log in to reply

– Rohit Shah · 2 years, 2 months ago

You are correct I did a silly mistake in both. I realized laterLog in to reply

– Tanishq Varshney · 2 years, 2 months ago

can u explain me the 5) oneLog in to reply

– Rohit Shah · 2 years, 2 months ago

Just draw the clock and reflect . Or you could subtract 12 hours from the given time(its effectively the same thing)Log in to reply

– Tanishq Varshney · 2 years, 2 months ago

then how is 25 replaced by 34 , why isnt it 35Log in to reply

– Sudeep Salgia · 2 years, 2 months ago

Another simple way which prevents confusion is that you subtract the given time from \( 11: 59 : 60 \) component wise. So here \( 11:59:60 - 04:25:37 = 07:34:23 \) which is the required answer.Log in to reply

– Azhaghu Roopesh M · 2 years, 2 months ago

Yeah, this is indeed the best way out .Log in to reply

– Rohit Shah · 2 years, 2 months ago

Because the seconds add up to give an extra minute. 37 + 23 is the extra minute. You could have used a similar reasoning that 4 + 7 is not 12 but we actually have got an extra hour by adding 25 and 35 mins. So sudeep has suggested a fast way of subtracting 12 hoursLog in to reply

@Deepanshu Gupta @Rohit Shah @Azhaghu Roopesh M @Raghav Vaidyanathan ,plz post a solution for the above problems – Tanishq Varshney · 2 years, 2 months ago

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