PHYC 2010 An electron microscopy study of Carabid beetles (H. E. Hinton and D. F

Question

PHYC 2010

An electron microscopy study of Carabid beetles (H. E. Hinton and D. F. Gibbs, Journal of Insect Physiology, vol 15, p 959, 1969) revealed the presence of ridge structures that act as diffraction gratings, giving rise to strong colour effects. In one section of the beetle the ridge structures were 1.4 micron apart. Find a value for the first-order diffraction angle for yellow light of wavelength 570 nm shining straight onto the ridge structures. An object is located 400 cm from a thin glass lens (n = 1.50) of diameter 25.0 mm that has both surfaces convex towards the object. One surface has radius of curvature, R_1 = 50.0 cm, and the other surface has radius of curvature, R_2 = 100.0 cm, as shown in the figure below. You can assume the thin lens approximation for this question. Calculate the focal length of the lens when in air. Is the lens a converging or a diverging lens? Explain briefly. With the aid of a diagram, show where the image will form. Calculate the distance from the lens to the position at which the image is formed. Calculate the transverse magnification of this image.

Explanation / Answer

Q 10.

a) distance between each ridge structure=1.4*10^(-6) m

wavelength=570 nm=570*10^(-9) m

as for diffraction grating,

d*sin(theta)=m*lambda

where d=distance between successive slits

theta=diffraction angle

lambda=wavelength

m=order of the diffraction angle

here m=1

so sin(theta)=0.407142

==>theta=24.025 degrees

part b:

i) as per lens makers formula, if focal length id f, then:

1/f=(n-1)*((1/R1)-(1/R2))

given that n=1.5

R1=0.5 m

R2=1 m

then 1/f=(1.5-1)*((1/0.5)-(1/1))=0.5

==>f=1/0.5=2 m

ii)as the focal length is positive, the lens is converging.

iv)

object distance=u=-400 cm=-4 m

focal length=f=2 m

then if image distance is v,

then (1/v)-(1/u)=1/f

==>(1/v)-(1/(-4))=1/2

==>v=4 m

hence the image will be formed 4 m at the other end of the lens

v)magnification=v/u=4/(-4)=-1

hence the image will be of same height , real and inverted in nature.

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.