Question 186: Ray Optics

Question

To find the focal length of a convex mirror, a student records the following data :
Object
Pin
Convex
Lens
Convex
Mirror
Image
Pin
22.2 cm
32.2 cm
45.8 cm
71.2 cm
The focal length of the convex lens is f
1
and that of mirror is f
2
. Then taking index correction to be negligibly small, f
1
and f
2
are close to :

Accepted Answer

For lens :
u
1
= $$-$$ (32.2 $$-$$ 22.2) cm
= $$-$$ 10 cm
v
1
= (71.2 $$-$$ 32.2) cm
= 39 cm
$$ 	herefore $$   $${1 \over {{f_1}}}$$ = $${1 \over {{v_1}}} - {1 \over {{u_1}}}$$
= $${1 \over {39}}$$ + $${1 \over {10}}$$
= $${{49} \over {390}}$$
$$ 	herefore $$   f
1
= 7.8 cm
For mirror :
R = (71.2 $$-$$ 45.8) cm
= 25.4 cm
$$ 	herefore $$   f
2
= $${R \over 2}$$ =  $${{25.4} \over 2}$$ = 12.7 cm

Answer

f
1
= 12.7 cm    f
2
= 7.8 cm

Answer

f
1
= 7.8 cm    f
2
= 12.7 cm

Answer

f
1
= 7.8 cm    f
2
= 25.4 cm

Answer

f
1
= 15.6 cm    f
2
= 25.4 cm

Ray Optics

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