Question

Find the position, nature and height of the image formed by a concave mirror of focal length 20cm when a 5cm size object is placed  in front of the mirror at  i) 20cm       ii) 40cm ​

Answer 1

It is given that,

It is given that,Focal length

It is given that,Focal lengthf=−20cm

It is given that,Focal lengthf=−20cmh i =3ho

It is given that,Focal lengthf=−20cmh i =3hoThe image is three times the size of the object.

So there are two cases.

Case 1. For real image

Case 1. For real imagem=-v/u=-3

Case 1. For real imagem=-v/u=-3v=3u

Case 1. For real imagem=-v/u=-3v=3uUsing mirror’s formula

Case 1. For real imagem=-v/u=-3v=3uUsing mirror’s formula1/f=1/v+1/u

Case 1. For real imagem=-v/u=-3v=3uUsing mirror’s formula1/f=1/v+1/u1/-20= 1/3u+1/u

Case 1. For real imagem=-v/u=-3v=3uUsing mirror’s formula1/f=1/v+1/u1/-20= 1/3u+1/uu=-480/3

Case 1. For real imagem=-v/u=-3v=3uUsing mirror’s formula1/f=1/v+1/u1/-20= 1/3u+1/uu=-480/3Case 2. For virtual image

Case 1. For real imagem=-v/u=-3v=3uUsing mirror’s formula1/f=1/v+1/u1/-20= 1/3u+1/uu=-480/3Case 2. For virtual imagem= u/−v =+3

Case 1. For real imagem=-v/u=-3v=3uUsing mirror’s formula1/f=1/v+1/u1/-20= 1/3u+1/uu=-480/3Case 2. For virtual imagem= u/−v =+3v=-3u

Case 1. For real imagem=-v/u=-3v=3uUsing mirror’s formula1/f=1/v+1/u1/-20= 1/3u+1/uu=-480/3Case 2. For virtual imagem= u/−v =+3v=-3uAgain using mirror’s formula

Case 1. For real imagem=-v/u=-3v=3uUsing mirror’s formula1/f=1/v+1/u1/-20= 1/3u+1/uu=-480/3Case 2. For virtual imagem= u/−v =+3v=-3uAgain using mirror’s formula1/-20=1/-3u+1/u

Case 1. For real imagem=-v/u=-3v=3uUsing mirror’s formula1/f=1/v+1/u1/-20= 1/3u+1/uu=-480/3Case 2. For virtual imagem= u/−v =+3v=-3uAgain using mirror’s formula1/-20=1/-3u+1/uu=-40/3cm

Case 1. For real imagem=-v/u=-3v=3uUsing mirror’s formula1/f=1/v+1/u1/-20= 1/3u+1/uu=-480/3Case 2. For virtual imagem= u/−v =+3v=-3uAgain using mirror’s formula1/-20=1/-3u+1/uu=-40/3cmThe possible values of u are

Case 1. For real imagem=-v/u=-3v=3uUsing mirror’s formula1/f=1/v+1/u1/-20= 1/3u+1/uu=-480/3Case 2. For virtual imagem= u/−v =+3v=-3uAgain using mirror’s formula1/-20=1/-3u+1/uu=-40/3cmThe possible values of u are 3/−80 cm and 3/−40 cm.

Case 1. For real imagem=-v/u=-3v=3uUsing mirror’s formula1/f=1/v+1/u1/-20= 1/3u+1/uu=-480/3Case 2. For virtual imagem= u/−v =+3v=-3uAgain using mirror’s formula1/-20=1/-3u+1/uu=-40/3cmThe possible values of u are 3/−80 cm and 3/−40 cm.Hence, this is the answer.

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