Relative M-cone and L-cone sensitivities read from the chapter's cone-sensitivity…

PHYSICS · Multi-part · Fermi University Physics · Biophysics & Medical Physics · Bioelectricity, the senses and the physics of the body · Bioelectricity, the senses and the physics of the body

Forces, Machines and Signals, Ch Vision and photoreception: counting photons

Problem

Relative M-cone and L-cone sensitivities read from the chapter's cone-sensitivity curves (dimensionless, S-cone sensitivity negligible at all three wavelengths below) are: at

550\,\mathrm{nm}

S_M=0.94

and

S_L=0.96

; at

580\,\mathrm{nm}

S_M=0.54

and

S_L=0.94

; at

600\,\mathrm{nm}

S_M=0.27

and

S_L=0.72

. A monochromatic yellow light at

580\,\mathrm{nm}

delivers

N_A

photons per second. It is to be matched by a mixture of a

550\,\mathrm{nm}

light delivering

N_1

photons per second and a

600\,\mathrm{nm}

light delivering

N_2

photons per second, using the cone-response rule

R_i = \sum_\lambda S_i(\lambda)\,(\text{photon rate at }\lambda)

. ((a)) Write the two equations (for

R_M

and

R_L

) that make the mixture a metamer of the monochromatic yellow. ((b)) Solve for

N_1/N_A

and

N_2/N_A

. ((c)) Explain, using univariance, why matching only

R_M

and

R_L

is enough here even though a third cone type exists.

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