Question

If an object is 30cm in front of a convex mirror that has a focal length of 60cm, how far behind the mirror will the image appear to an observer? How tall will the image be?​

Answer 1

Given :-

• Focal length = 60cm

• Distance btw. mirror and object = v = 30cm

To find :-

• How far behind the mirror will the image appear to an observer?
• How tall will the image be?

Solution:-

Since , the mirror is a Convex Mirror

Focal length = + 60 cm

u = - 30cm ( since the object will be placed on the negative side )

Now;

Distance btw. the image and mirror = + v ( since it is given that image will be formed behind the mirror )

Acc. to the mirror formula ;

$\sf{\star{\large{\boxed{\orange{\mathsf{ \dfrac{1}{f} = \dfrac{1}{u}+ \dfrac{1}{v}}}}}}}$

$\sf{\star{\large{\boxed{\pink{\mathrm{ Magnification = - \dfrac{ v }{u}}}}}}}$

$\sf \implies \dfrac{1}{60} = \dfrac{1}{-30} + \dfrac{1}{v}$

$\sf \implies \dfrac{1}{v} = \dfrac{ 1 }{60} + \dfrac{1}{30}$

$\sf \implies \dfrac{1}{v} = \dfrac{1 + 2 }{60}$

$\sf \implies \dfrac{1}{v} = \dfrac{3}{60}$

$\sf \implies \dfrac{1}{v} = \dfrac{1}{20}$

$\sf \implies v = 20 cm$

$\sf{\dag{\large{\boxed{\red{\bold{Image\: will \: be \: formed \: 20cm \: behind \:the \: mirror }}}}}}$

we know That ;-

$\sf{\star{\large{\boxed{\pink{\mathrm{ Magnification = - \dfrac{ v }{u}}}}}}}$

Therefore;

Magnification = - ( -20 ) / 30

Magnification = 20 / 30

Magnification = 2 / 3

$\sf{\dag{\large{\boxed{\red{\bold{Image\: will \: be \: small \: in \: size \:in \: ratio \: 2 : 3 }}}}}}$

$\underline{\boxed{\purple{\sf Answer: }}}$

• Image will be formed 20 cm behind the mirror
• Image will be smaller in size then the object by 0.67x

Answer 2

Answer:

Here U=-60cm ( distance of object from optical centre considering sign conventions also)

f=+30 cm ( positive for convex lens)

STEP1) Considering first only the image formation by lens :

We have lens formula as -1/u+1/v=1/f

-(1/-60)+1/v=1/30

1/v=1/30–1/60

1/v=1/60

V=60 cm( distance of image formed on the other side of lens)

STEP2)Image formation by mirror

U(distance of object)= 60–10 =50 cm (object is virtual here so real image will be formed by plane mirror)

V(image distance)=50 cm in front of mirror OR 40 cm from optical centre of lens on the other side of lens .

STEP3) image formation by lens again:

U=object distance =+40 cm (object is virtual )

f=+30 cm

V=?

Using lens formula again

-1/40+1/V=1/30

1/v=7/120

V=17.14cm

So finally image is formed at a distance of 17.14 cm from the optical centre of lens on the object’s side .

The distance of image from object is equal to

60–17.14=44.86 cm...

.

Hope it's helps... ⤴️

$\huge\red{\boxed{\blue{\mathcal{\overbrace{\underbrace{\fcolorbox{blue}{aqua}{\underline{\red{Mr Kapil}}}}}}}}}$

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