Question

I’m playing with the optics kit we bought my eldest daughter when she was four. The set contains a diverging lens made out of some kind of glass with index of refraction of about 1.6. The focal length of the lens is |f| = 5cm. One surface of the lens is planar and the other is curved. What is the radius of curvature of the curved surface? Assume light reaches the curved surface first and report the radius of curvature with the correct sign.

(a) 3cm
(b) −3cm
(c) 6cm
(d) −6cm
(e) Toby.

Answer 1

(b)-3 cm

Step-by-step explanation:

We are given that

Focal length,
`\mid f\mid=5 cm`

Refractive index=n=1.6

Radius of curvature of plane surface=
`R_1=0`

Radius of curvature of curved surface=
`R_2`

Lens maker formula

`(1)/(f)=(n-1)((1)/(R_1)-(1)/(R_2))`

Substitute the values

`(1)/(5)=(1.6-1)(0-(1)/(R_2))`

`0.2=0.6(-(1)/(R_2))`

`R_2=-(0.6)/(0.2)=-3 cm`

Option (b) is true.