Question:

Your client is thecurator of the local museum and as such is responsible for the waythe various objects are displayed. Usually, the items are displayedinside the large, clear Poly(methyl methacrylate) (PMMA)1 displaycabinets which are already installed in the museum, however, yourclient recently received a rare collection of butterflies which arehoused in their own Polyethylene terephthalate (PET) glass case andshe is considering which is the best way to display this item. Doesshe:

(i) Leave the buttercollection in its glass case and display this as is on top of astand?

(ii) Remove thebutterfly collection from its case and place the collection insidethe existing large display cabinet?

(iii) Leave thedisplay in its glass case and place this inside the existing largedisplay cabinet, in which case visitors would be looking at thebutterfly collection through two layers of glass? In order toassist your client in making this decision, you do some thinkingand quick calculations.

1. PMMA is also known as acrylic or acrylic glass.

a) In relation tovisitors’ ability to see the collection under the glass, what isthe significance of the two different refractive indices? Explainin detail.

b) Presuming thebutterfly case is placed inside the museum display cabinet (as perOption

(iii)), what is thecritical angle for light passing through the two layers ofglass?

c) If the situationwas reversed, and the butterfly case was made of PMMA and themuseum display cabinet was made of PET, what would be the criticalangle for light passing through the two layers of glass? Again,assume the butterfly case is placed inside the museum displaycabinet.

d) After carefulexploration of the situation and based on the above considerations,which option would you recommend your client select? Explain indetail.

Take the refractiveindex of the PET butterfly case to be 1.5750 and the refractiveindex of the existing PMMA museum display cabinets to be1.4893.